// Numbas version: finer_feedback_settings
{"name": "Uegentlige integraler", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "questions": [{"name": "Bestemte eller uegentlige integraler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Hvilke av f&oslash;lgende integraler kan regnes ut direkte ved bruk av formelen $\\int\\limits_a^bf(x)\\mathrm dx=F(b)-F(a)$ hvor $F'(x)=f(x)$</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": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\int\\limits_0^1 \\ln x\\mathrm dx$", "$\\int\\limits_3^5 \\ln x\\mathrm dx$", "$\\int\\limits_0^2 \\frac{1}{(x-1)^2}\\mathrm dx$", "$\\int\\limits_0^1 \\ln(x+1)\\mathrm dx$", "$\\int\\limits_0^{\\pi} \\tan x\\mathrm dx$"], "matrix": [0, "1", 0, "1", 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "integralet fra graf", "extensions": [], "custom_part_types": [], "resources": [["question-resources/uegentlig_integral_omr\u00e5det.PNG", "/srv/numbas/media/question-resources/uegentlig_integral_omr\u00e5det.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>La $f:(0,\\infty)\\rightarrow \\mathbb{R}$ v&aelig;re en kontinuerlig funksjon.</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": "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>Se p&aring; bildet og velg hvilken p&aring;stand som er riktig om arealet til det skraverte omr&aring;det&nbsp;</p>\n<p><img src=\"resources/question-resources/uegentlig_integral_omr&aring;det.PNG\"/></p>\n<p></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Arealet er uendelig", "Arealet er endelig og er likt det&nbsp;uegentlige integralet $\\int\\limits_2^{\\infty}f(x)\\mathrm{d}x$", "Arealet avhenger av den antideriverte til funksjonen $f$ og grenseverdien $\\lim_\\limits{b\\rightarrow\\infty}F(b)$"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Konvergens eller divergens", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>La $f:[a,\\infty)\\rightarrow \\mathbb{R}$ v&aelig;re en kontinuerlig funksjon.&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, "prompt": "<p>I definisjon av det uegentlige integralet av $f$ setter vi opp grenseverdien&nbsp;</p>\n<p>$\\int\\limits_a^{\\infty}f(x)\\mathrm{d}x=\\lim\\limits_{b\\rightarrow\\infty}\\int\\limits_a^b f(x)\\mathrm{d}x$.</p>\n<p>Anta grenseverdien $\\lim\\limits_{b\\rightarrow\\infty}\\int\\limits_a^bf(x)\\mathrm{d}x$ ikke eksisterer. Hvilken eller hvilke p&aring;stander er da riktige?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Man m&aring; finne en annen passende regneteknikk for &aring; bestemme integralet", "Integralet&nbsp;$\\int\\limits_a^{\\infty}f(x)\\mathrm{d}x$ konvergerer", "Integralet&nbsp;$\\int\\limits_a^{\\infty}f(x)\\mathrm{d}x$ divergerer", "Integralet&nbsp;$\\int\\limits_a^{\\infty}f(x)\\mathrm{d}x$&nbsp;eksisterer ikke"], "matrix": [0, 0, "1", "1"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "teorem om konvergensen divergensen for f>g", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>La $f:[a,\\infty)\\rightarrow\\mathbb{R}$ og&nbsp;$g:[a,\\infty)\\rightarrow\\mathbb{R}$ v&aelig;re kontinuerlige og positive funksjoner, slik at $f(x)\\geq g(x)$ i $[a,\\infty)$.</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": "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>La oss anta at $\\int\\limits_a^{\\infty}f(x)\\mathrm dx$ konvergerer. Velg hvilken p&aring;stand som er riktig</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$ konvergerer", "$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$ divergerer", "Man kan ikke si noe om konvergensen av&nbsp;$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$"], "matrix": ["1", "0", 0], "distractors": ["", "", ""]}, {"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>La oss anta at $\\int\\limits_a^{\\infty}f(x)\\mathrm dx$ divergerer. Velg hvilken p&aring;stand som da er riktig</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$ konvergerer", "$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$ divergerer", "Man kan ikke si noe om konvergensen av&nbsp;$\\int\\limits_a^{\\infty}g(x)\\mathrm dx$"], "matrix": ["0", "0", "1"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Uegentlig integral av 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": "None specified"}, "statement": "<p>Fra kalkulus 1 vet vi at $\\int\\limits_{-b}^bx\\mathrm dx=\\frac{x^2}{2}\\Big|_{-b}^b=\\frac{b^2}{2}-\\frac{(-b)^2}{2}=0$</p>", "advice": "", "rulesets": {}, "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, "prompt": "<p>Hva kan man si om uegentlige integralet $\\int\\limits_{-\\infty}^{\\infty}x\\mathrm dx$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Integralet&nbsp;$\\int\\limits_{-\\infty}^{\\infty}x\\mathrm dx$ er likt et endelig tall men ikke 0", "Integralet&nbsp;$\\int\\limits_{-\\infty}^{\\infty}x\\mathrm dx$ er likt 0", "Integralet&nbsp;$\\int\\limits_{-\\infty}^{\\infty}x\\mathrm dx$ divergerer&nbsp;", "Integralet&nbsp;$\\int\\limits_{-\\infty}^{\\infty}x\\mathrm dx$ eksisterer ikke fordi integralet&nbsp;$\\int\\limits_{0}^{\\infty}x\\mathrm dx$ divergerer"], "matrix": [0, 0, "1", "1"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}], "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": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "type": "exam", "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/uegentlig_integral_omr\u00e5det.PNG", "/srv/numbas/media/question-resources/uegentlig_integral_omr\u00e5det.PNG"]]}