// Numbas version: exam_results_page_options
{"name": "Numbastest uke 36: Kontinuitet og grenser", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Injektive funksjoner", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sirkelen.PNG", "/srv/numbas/media/question-resources/sirkelen.PNG"], ["question-resources/parabel.PNG", "/srv/numbas/media/question-resources/parabel.PNG"], ["question-resources/to_mengder_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_funksjon.PNG"], ["question-resources/to_mengder_ikke_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_ikke_funksjon.PNG"], ["question-resources/Sin.PNG", "/srv/numbas/media/question-resources/Sin.PNG"], ["question-resources/to_mengder_funksjon_injektiv.PNG", "/srv/numbas/media/question-resources/to_mengder_funksjon_injektiv.PNG"], ["question-resources/rot_fLiH8fE.PNG", "/srv/numbas/media/question-resources/rot_fLiH8fE.PNG"], ["question-resources/eksp.PNG", "/srv/numbas/media/question-resources/eksp.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Hvilke av funksjoner av $x$ under er injektive (har en invers)?&nbsp;</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$x$ er lengden av foten i cm\n<div>&nbsp; &nbsp; $y$ er skost&oslash;rrelse&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</div>", "$x$ er din medstudent<br/>$y$ er hans/hennes bursdagen", "$x-7y=58$", "$y=x^2-4$", "<img src=\"resources/question-resources/Sin.PNG\" width=\"223\" height=\"160\"/>", "<img src=\"resources/question-resources/parabel.PNG\" width=\"197\" height=\"197\"/>", "<table style=\"height: 36px; border-style: none; border-color: #000000;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 27px; height: 18px;\">$x$</td>\n<td style=\"width: 25px; height: 18px;\">-7</td>\n<td style=\"width: 18px; height: 18px;\">-2</td>\n<td style=\"width: 16px; height: 18px;\">0</td>\n<td style=\"width: 18px; height: 18px;\">7</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 27px; height: 18px;\">$y$</td>\n<td style=\"width: 25px; height: 18px;\">-22</td>\n<td style=\"width: 18px; height: 18px;\">-22</td>\n<td style=\"width: 16px; height: 18px;\">8</td>\n<td style=\"width: 18px; height: 18px;\">15</td>\n</tr>\n</tbody>\n</table>", "<table style=\"height: 36px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$x$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-2</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">7</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">8</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$y$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">3</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-14</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">11</td>\n</tr>\n</tbody>\n</table>", "<table style=\"height: 36px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$x$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-7</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">-2</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">0</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">7</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 16px; text-align: center; height: 18px;\">$y$</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n<td style=\"width: 16px; text-align: center; height: 18px;\">15</td>\n</tr>\n</tbody>\n</table>", "<img src=\"resources/question-resources/to_mengder_funksjon.PNG\" width=\"210\" height=\"163\"/>", "$y=\\sqrt{x}$", "<img src=\"resources/question-resources/to_mengder_funksjon_injektiv.PNG\" width=\"209\" height=\"164\"/>", "<img src=\"resources/question-resources/rot_fLiH8fE.PNG\" width=\"287\" height=\"215\"/>", "<img src=\"resources/question-resources/eksp.PNG\" width=\"274\" height=\"236\"/>"], "matrix": ["0", "0", "0.5", 0, 0, "0", "0", "0.5", "0", "0", "0.5", "0.5", "0.5", "0.5"], "distractors": ["", "", "", "", "", "", "", "", "", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Velg kontinuerlige funksjoner", "extensions": [], "custom_part_types": [], "resources": [["question-resources/exp.PNG", "/srv/numbas/media/question-resources/exp.PNG"], ["question-resources/rasjonal.PNG", "/srv/numbas/media/question-resources/rasjonal.PNG"], ["question-resources/sign_x.PNG", "/srv/numbas/media/question-resources/sign_x.PNG"], ["question-resources/sin_og_x2.PNG", "/srv/numbas/media/question-resources/sin_og_x2.PNG"], ["question-resources/x2.PNG", "/srv/numbas/media/question-resources/x2.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Hvilke av f&oslash;lgende funksjoner er kontinuerlige innenfor deres definisjonsmengder?</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["&nbsp;<img src=\"resources/question-resources/exp.PNG\" width=\"310\" height=\"276\"/>&nbsp; med $D_f=\\mathbb{R}$", "<img src=\"resources/question-resources/rasjonal.PNG\" width=\"321\" height=\"279\"/> med $D_f=\\mathbb{R}\\setminus \\{0\\}$", "<img src=\"resources/question-resources/sign_x.PNG\" width=\"328\" height=\"192\"/> med $D_f=\\mathbb{R}$", "<img src=\"resources/question-resources/sin_og_x2.PNG\" width=\"336\" height=\"263\"/> med $D_f=\\mathbb{R}\\setminus \\{2\\}$", "<img src=\"resources/question-resources/x2.PNG\" width=\"336\" height=\"373\"/> med $D_f=\\mathbb{R}$"], "matrix": ["0.5", "0.5", 0, "0.5", "0.5"], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Grenselover", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn f&oslash;lgende grenseverdier</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5 except a)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{a}}\\var{b}=$</p>", "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{a}}x=$</p>", "minValue": "{a}", "maxValue": "{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{a}}|x|=$</p>", "minValue": "{abs(a)}", "maxValue": "{abs(a)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Det er gitt en funksjon $sign(x) = \\begin{cases} -1, &amp; \\mbox{n&aring;r } x&lt;0 \\\\ 0, &amp; \\mbox{n&aring;r } x=0\\\\ 1, &amp; \\mbox{n&aring;r } x&gt;0 \\end{cases}$</p>\n<p>$\\lim\\limits_{x\\rightarrow0^-}sign(x)=$[[0]]</p>\n<p>$\\lim\\limits_{x\\rightarrow0^+}sign(x)=$[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-1", "maxValue": "-1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Finn grenseverdier (for kontinuerlige funksjoner)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn f&oslash;lgende grenseverdier</p>", "advice": "", "rulesets": {}, "variables": {"g1": {"name": "g1", "group": "Ungrouped variables", "definition": "random(-2..2)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2 .. 6#4)", "description": "", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-6..6 except b except c)", "description": "", "templateType": "anything"}, "g2": {"name": "g2", "group": "Ungrouped variables", "definition": "random(-4..4 except d)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["g1", "a", "b", "c", "k", "d", "g2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{g1}}\\simplify{{a}x^2+{b}x+{c}}=$</p>", "minValue": "{a*(g1^2)+b*g1+c}", "maxValue": "{a*(g1^2)+b*g1+c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\frac{\\pi}{\\var{k}}}\\simplify{{a} sin(x)}=$</p>", "minValue": "{a*sin(pi/k)}", "maxValue": "{a*sin(pi/k)}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{g2}}\\dfrac{\\simplify{{a}x^2-{a*(b+c)}x+{a*b*c}}}{\\simplify{x-{d}}}$</p>", "minValue": "{(a*g2*g2-(a*b+a*c)*g2+a*b*c)/(g2-d)}", "maxValue": "{(a*g2*g2-(a*b+a*c)*g2+a*b*c)/(g2-d)}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Grenselover 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Anta at $\\lim\\limits_{x\\rightarrow\\var{a}}f(x)=\\var{b}$ og $\\lim\\limits_{x\\rightarrow\\var{a}}g(x)=\\var{c}$ og at $f$ er kontinuerlig i $x=\\var{c}$.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5 except c)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn f&oslash;lgende grenseverdier</p>\n<p>$\\lim\\limits_{x\\rightarrow\\var{a}}[f(x)+g(x)]=$[[0]]</p>\n<p>$\\lim\\limits_{x\\rightarrow\\var{a}}[f(x)-g(x)]=$[[1]]</p>\n<p>$\\lim\\limits_{x\\rightarrow\\var{a}}[f(x)\\cdot g(x)]=$[[2]]</p>\n<p>$\\lim\\limits_{x\\rightarrow\\var{a}}\\frac{f(x)}{g(x)}=$[[3]]</p>\n<p>$\\lim\\limits_{x\\rightarrow\\var{a}}f(g(x))=f($[[4]]$)$</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b+c}", "maxValue": "{b+c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b-c}", "maxValue": "{b-c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b*c}", "maxValue": "{b*c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b/c}", "maxValue": "{b/c}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Finn grenseverdier (for x-> uendelig)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn f&oslash;lgende grenseverdier (Notasjon: For $\\infty$ skriv inn infty)</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(-5..5 except 0 except k1)", "description": "", "templateType": "anything", "can_override": false}, "p1": {"name": "p1", "group": "Ungrouped variables", "definition": "random(6..10)", "description": "", "templateType": "anything", "can_override": false}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "l1": {"name": "l1", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "l2": {"name": "l2", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "l3": {"name": "l3", "group": "Ungrouped variables", "definition": "random(-5..5 except 0 except l1)", "description": "", "templateType": "anything", "can_override": false}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "p1-2", "description": "", "templateType": "anything", "can_override": false}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "random(2..5 except q1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k1", "k2", "k3", "p1", "p2", "l1", "l2", "l3", "q1", "q2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\infty}\\dfrac{1}{x}$</p>", "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\infty}\\dfrac{\\simplify{{k1}x^{p1}+{k2}x^{p2}+{k3}}}{\\simplify{{l1}x^{q1}+{l2}x^{q2}+{l3}}}$</p>", "answer": "infty", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\infty}\\dfrac{\\simplify{{l1-1}x^{p1-1}+{k2}x^{q2}+{l3}}}{\\simplify{{k1}x^{p1}+{l2}x^{p2}+{k3}}}$</p>", "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\infty}\\dfrac{\\simplify{{l3}x^{p1}+{k2}x^{q2-1}+{k1}}}{\\simplify{{k3}x^{p1}+{l2}x^{p2}+{l1}}}$</p>", "minValue": "{l3/k3}", "maxValue": "{l3/k3}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Finn grenseverdier (for 0/0)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Finn f&oslash;lgende grenseverdier</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"g1": {"name": "g1", "group": "Ungrouped variables", "definition": "random(-2..2)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2 .. 6#4)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-6..6 except b except c)", "description": "", "templateType": "anything", "can_override": false}, "g2": {"name": "g2", "group": "Ungrouped variables", "definition": "random(-4..4 except d)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["g1", "a", "b", "c", "k", "d", "g2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{c}}\\dfrac{\\simplify{x^2-{c^2}}}{\\simplify{x-{c}}}$</p>", "minValue": "{2*c}", "maxValue": "{2*c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\lim\\limits_{x\\rightarrow\\var{d}}\\dfrac{\\simplify{{a}x^2-{a*(d+c)}x+{a*d*c}}}{\\simplify{x^2-{d^2}}}$</p>", "minValue": "{(a*(d-c))/(2*d)}", "maxValue": "{(a*(d-c))/(2*d)}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "x=0 for 1/x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Det er gitt en funksjon $f(x)=\\dfrac{1}{x}$</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$x=0$ blir</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["et punkt hvor funksjonen er diskontinuerlig", "et nullpunkt", "den verikale asymptoten", "den horisontale asymptoten"], "matrix": [0, 0, "1", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Asymptoter definisjon", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>La $f(x)$ v&aelig;re en funksjon og $a,b,c,d\\in\\mathbb{R}$.</p>\n<p>La</p>\n<p>1) $\\lim\\limits_{x\\rightarrow a}f(x)=\\infty$&nbsp;</p>\n<p>2) $\\lim\\limits_{x\\rightarrow \\infty}f(x)=b$&nbsp;</p>\n<p>3) $\\lim\\limits_{x\\rightarrow\\infty}(f(x)-(cx+d))=0$</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Velg likningene til asymptotene</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Vertikal asymptote", "Horisontal asymptote&nbsp;", "Skr&aring; asymptote"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["$x=a$", "$x=b$", "$y=a$", "$y=b$", "$y=ax+b$", "$y=cx+d$", "$x=ay+b$", "$x=cy+d$"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/sirkelen.PNG", "/srv/numbas/media/question-resources/sirkelen.PNG"], ["question-resources/parabel.PNG", "/srv/numbas/media/question-resources/parabel.PNG"], ["question-resources/to_mengder_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_funksjon.PNG"], ["question-resources/to_mengder_ikke_funksjon.PNG", "/srv/numbas/media/question-resources/to_mengder_ikke_funksjon.PNG"], ["question-resources/Sin.PNG", "/srv/numbas/media/question-resources/Sin.PNG"], ["question-resources/to_mengder_funksjon_injektiv.PNG", "/srv/numbas/media/question-resources/to_mengder_funksjon_injektiv.PNG"], ["question-resources/rot_fLiH8fE.PNG", "/srv/numbas/media/question-resources/rot_fLiH8fE.PNG"], ["question-resources/eksp.PNG", "/srv/numbas/media/question-resources/eksp.PNG"], ["question-resources/exp.PNG", "/srv/numbas/media/question-resources/exp.PNG"], ["question-resources/rasjonal.PNG", "/srv/numbas/media/question-resources/rasjonal.PNG"], ["question-resources/sign_x.PNG", "/srv/numbas/media/question-resources/sign_x.PNG"], ["question-resources/sin_og_x2.PNG", "/srv/numbas/media/question-resources/sin_og_x2.PNG"], ["question-resources/x2.PNG", "/srv/numbas/media/question-resources/x2.PNG"]]}