// Numbas version: exam_results_page_options
{"name": "True/false statements about continuity of a function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0, "questions": []}], "name": "True/false statements about continuity of a function", "ungrouped_variables": ["del", "ep"], "showQuestionGroupNames": false, "functions": {}, "tags": ["checked2015", "MAS2224"], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"del": {"name": "del", "group": "Ungrouped variables", "definition": "random('$\\\\epsilon$','$\\\\chi$','$\\\\rho$','$\\\\omega$')", "description": "", "templateType": "anything"}, "ep": {"name": "ep", "group": "Ungrouped variables", "definition": "random('$\\\\alpha$','$\\\\beta$','$\\\\gamma$','$\\\\delta$')", "description": "", "templateType": "anything"}}, "statement": "<p>Let $x_0$ be a point in the open interval $I \\subset \\mathbb{R}$ and let $f:I \\setminus \\{x_0\\} \\rightarrow \\mathbb{R}$ be a function.</p>\n<p>What does it mean to say that $f(x) \\rightarrow a$ as $x \\rightarrow x_0$?</p>", "parts": [{"type": "gapfill", "scripts": {}, "marks": 0, "prompt": "\n<p>Choose one of the following as the correct definition:</p>\n<p></p>\n<p>[[0]]</p>\n", "showCorrectAnswer": true, "gaps": [{"type": "1_n_2", "maxMarks": 0, "marks": 0, "displayColumns": 1, "minMarks": 0, "distractors": ["", "", "", "", "", ""], "shuffleChoices": true, "scripts": {}, "displayType": "radiogroup", "choices": ["<p>For every $\\var{ep} \\gt 0$ , there exists a $\\var{del} \\gt 0$ such that $\\left |f(x)-a\\right | \\lt \\var{ep}$ whenever $0 \\lt |x-x_0| \\lt \\var{del}$ and $x \\in I$.</p>", "<p>For every $\\var{del} \\gt 0$ , there exists a $\\var{ep} \\gt 0$ such that $\\left |f(x)-a\\right | \\lt \\var{ep}$ whenever $0 \\lt |x-x_0| \\lt \\var{del}$ and $x \\in I$.</p>", "<p>For every $\\var{ep} \\gt 0$ , there exists a $\\var{del} \\gt 0$ such that $\\left |f(x)-a\\right | \\lt \\var{del}$ whenever $0 \\lt |x-x_0| \\lt \\var{ep}$ and $x \\in I$.</p>", "<p>For every $\\var{ep} \\gt 0$ , there exists a $\\var{del} \\gt 0$ such that $\\left |f(x)-f(x_0)\\right | \\lt \\var{ep}$ whenever $0 \\lt |x-a| \\lt \\var{del}$ and $x \\in I$.</p>", "<p>For every $\\var{del} \\gt 0$ , there exists a $\\var{ep} \\gt 0$ such that $\\left |f(x)-a\\right | \\gt \\var{del}$ whenever $0 \\lt |x-x_0| \\lt \\var{ep}$ and $x \\in I$.</p>", "<p>For every $\\var{ep} \\gt 0$ , there exists a $\\var{del} \\gt 0$ such that $\\left |f(x)-a\\right | \\lt \\var{ep}$ whenever $0 \\lt |x-x_0| \\gt \\var{del}$ and $x \\in I$.</p>"], "showCorrectAnswer": true, "matrix": [2, 0, 0, 0, 0, 0]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}