// Numbas version: exam_results_page_options
{"name": "True/false statements about continuity and differentiability, ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "\n  \n  \n  <p>[[0]]</p>\n  \n  \n  \n", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"displayType": "checkbox", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "minAnswers": 0, "minMarks": 0, "shuffleAnswers": false, "variableReplacements": [], "layout": {"expression": ""}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "matrix": [[1, -1], [1, -1], ["-1", "1"], [-1, 1]], "choices": ["<p>{Ch1}</p>", "<p>{Ch2}</p>", "<p>{Ch3}</p>", "<p>{Ch4}</p>"], "unitTests": [], "answers": ["True", "False"], "scripts": {}, "maxMarks": 0, "showCorrectAnswer": true, "marks": 0, "warningType": "none"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}], "variables": {"v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3)", "name": "v", "description": ""}, "f1": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p>If&nbsp;a function $f: \\\\mathbb{R} \\\\to \\\\mathbb{R}$ is continuous at $c \\\\in \\\\mathbb{R}$, then it is differentiable at $c$.</p>\"", "name": "f1", "description": ""}, "ch2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(u=1,tr4,if(u=2,tr5,tr6))", "name": "ch2", "description": ""}, "u": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3)", "name": "u", "description": ""}, "f2": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p><span>If a function $f: \\\\mathbb{R} \\\\to \\\\mathbb{R}$ is continuous </span><span>on $(a,b)$ and $f(a) &lt; 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\\\\gamma &lt; f(b)$, then $f(c)=\\\\gamma$ for some $c \\\\in (a,b)$.</span></p>\"", "name": "f3", "description": ""}, "tr5": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p><span>If a function $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, &nbsp;then $f\\'(c)=\\\\dfrac{f(b)-f(a)}{b-a}$ for some $c \\\\in (a,b)$.</span></p>\"", "name": "tr5", "description": ""}, "ch1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(t=1,tr1,if(t=2,tr2,tr3))", "name": "ch1", "description": ""}, "f5": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p><span>If a function $f$ is differentiable on $(a,b)$, &nbsp;then $f\\'(c)=\\\\dfrac{f(b)-f(a)}{b-a}$&nbsp;</span>for some $c \\\\in (a,b)$.</p>\"", "name": "f5", "description": ""}, "tr2": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p>If a function $f$ is continuous on $[a,b]$ and $f(a) &lt; \\\\gamma &lt; f(b)$, then $f(c)=\\\\gamma$ for some $c \\\\in (a,b)$.</p>\"", "name": "tr2", "description": ""}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3)", "name": "f", "description": ""}, "tr3": {"templateType": "long string", "group": "Ungrouped variables", "definition": "\"<p><span>If a function $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, and if $f(a) &lt; 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Note that every correct answer is worth 1 mark, but every wrong answer loses a mark.</p>", "tags": ["checked2015", "continuous", "convergence", "convergent sequences", "limits", "sequence", "sequences"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.</p>\n<p>Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct,&nbsp; but the feedback indicates that the third was wrong.</p>"}, "advice": "<p>You should be able to work out the correct answers from your notes.</p>", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}