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{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.4.3.2 catenary function", "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": {}, "extensions": [], "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, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["one-to-one", "many-to-one"], "matrix": [0, "1"], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part c)", "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 a continuous or discontinuous function</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["continuous", "discontinuous"], "matrix": ["1", 0], "distractors": ["", ""]}, {"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>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", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}