// Numbas version: exam_results_page_options {"name": "HELM Book 2.4.1 Exercises", "metadata": {"description": "

Exercises for HELM Book 2.4.1

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.

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Study the graph of the function $y=\\var{fn}$. Is this a continuous function?

", "advice": "

The function $y=\\var{fn}$ is continuous.

\n

{diagram}

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Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Draw a graph of the function

\n

$f(x)=\\begin{cases}\\var{case1}\\quad & x<\\var{a}\\\\\\var{case2}\\quad & x=\\var{a}\\\\\\var{case3}\\quad & x>\\var{a}\\end{cases}$

\n

Then compute each of the following limits. If a limit does not exist, type DNE into the box.

", "advice": "

$f(x)=\\begin{cases}\\var{case1}\\quad & x<\\var{a}\\\\\\var{case2}\\quad & x=\\var{a}\\\\\\var{case3}\\quad & x>\\var{a}\\end{cases}$

\n

{diagram}

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Find $\\lim\\limits_{x\\to \\var{am1} ^+}f(x)$

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Find $\\lim\\limits_{x\\to \\var{am1} ^-}f(x)$

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Find $\\lim\\limits_{x\\to \\var{am1}}f(x)$

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Find $\\lim\\limits_{x\\to \\var{a}^+}f(x)$

", "answer": "{case3endpoint}", "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": "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": "

Find $\\lim\\limits_{x\\to \\var{a}^-}f(x)$

", "answer": "{case1endpoint}", "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": "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": "

Find $\\lim\\limits_{x\\to \\var{a}}f(x)$

", "answer": "{lim}", "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": []}], "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", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "

This quiz is a Numbas implementation of the Helping Engineers Learn Maths (HELM) booklet 2.4, Characterising functions exercises.

\n

Questions generally have multiple versions, clicking the \"Try another question like this one\" button will generate a new version.

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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