// 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": [{"parts": [{"scripts": {}, "gaps": [{"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>"], "matrix": [2, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", ""], "shuffleChoices": true, "scripts": {}, "maxMarks": 0, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 1, "marks": 0}], "type": "gapfill", "prompt": "\n<p>Choose one of the following as the correct definition:</p>\n<p></p>\n<p>[[0]]</p>\n", "showCorrectAnswer": true, "marks": 0}], "variables": {"del": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random('$\\\\epsilon$','$\\\\chi$','$\\\\rho$','$\\\\omega$')", "name": "del", "description": ""}, "ep": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random('$\\\\alpha$','$\\\\beta$','$\\\\gamma$','$\\\\delta$')", "name": "ep", "description": ""}}, "ungrouped_variables": ["del", "ep"], "rulesets": {}, "name": "True/false statements about continuity of a function", "functions": {}, "variable_groups": [], "showQuestionGroupNames": false, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "tags": ["checked2015", "MAS2224"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "advice": "", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}