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{"name": "HELM Book 2.4.3 Exercises", "metadata": {"description": "<p>Exercises for HELM Book 2.4.3</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "2.4.3.1 Odd, even or neither", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Identify whether a function is odd, even or neither from its graph. Part of HELM Book 2.4.3.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Is the function $f(x)=\\var{fn}$ odd, even or neither? If necessary sketch a graph to help you.</p>", "advice": "<p>$f(x)=\\var{fn}$</p>\n<p>{diagram}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"fn": {"name": "fn", "group": "Ungrouped variables", "definition": "expression([\n    string(6),\n    \"x^2\",\n    \"2x+1\",\n    \"x\",\n    \"2x\"][idx])", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "[\"even\",\"even\",\"neither\",\"odd\",\"odd\"][idx]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything", "can_override": false}, "diagram": {"name": "diagram", "group": "Ungrouped variables", "definition": "jsxgraph(\n  500,500,\n  [-10, 20, 10,-20],\n  [\n    \"f\":['functiongraph',[fn]]\n  ]\n)  ", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["fn", "ans", "idx", "diagram"], "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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["odd", "even", "neither"], "matrix": ["if(ans=\"odd\",1,0)", "if(ans=\"even\",1,0)", "if(ans=\"neither\",1,0)"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "2.4.3.2 catenary function", "extensions": [], "custom_part_types": [], "resources": [["question-resources/HELM2_4_3_2.png", "/srv/numbas/media/question-resources/HELM2_4_3_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Characterise the cosh function as continuous, many-to-one, even, and find the limit as x approaches 1. Part of HELM book 2.4.3.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The diagram below represents a heavy cable hanging under gravity from two points at the same height. Such a curve (shown as a dashed line), known as a <strong>catenary</strong>, is described by a mathematical function known as a hyperbolic cosine, $f(x) = cosh x$, discussed in HELM 6.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/HELM2_4_3_2.png\"/></p>", "advice": "<p>The $\\cosh(x)$ function is a continous, many-to-one even function (it is symmetric about the $y$-axis).</p>\n<p>As $x\\to 0,\\;\\cosh(x) \\to 1$.</p>", "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": true, "customName": "Part a)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Comment upon any symmetry.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["The function is odd.", "The function is even.", "The function is neither odd nor even."], "matrix": [0, "1", 0], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part b)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Is this function one-to-one or many-to-one?</p>", "minMarks": 0, "maxMarks": 0, 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"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>State $\\lim\\limits_{x\\to 0}\\cosh x$.</p>", "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "menu", "onleave": {"action": "none", 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