// Numbas version: exam_results_page_options
{"name": "Evaluate a limit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b"], "name": "Evaluate a limit", "tags": [], "advice": "<p style=\"padding-left: 60px;\">\\(\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{x^2-\\simplify{{a}+{b}}x+\\simplify{{a}*{b}}}\\)</p>\n<p style=\"padding-left: 30px;\">We can factorise the denominator</p>\n<p style=\"padding-left: 60px;\">\\(\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{(x-\\var{a})(x-\\var{b})}\\)</p>\n<p style=\"padding-left: 30px;\">Cancel out the common factor</p>\n<p style=\"padding-left: 60px;\">\\(\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{1}{x-\\var{b}}\\)</p>\n<p style=\"padding-left: 30px;\">Insert the value \\(\\var{a}\\) in for \\(x\\) to evaluate the limit</p>\n<p style=\"padding-left: 60px;\">\\(-\\frac{1}{\\simplify{{b}-{a}}}\\)</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>Input your answer as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/({a}-{b})", "minValue": "1/({a}-{b})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "extensions": [], "statement": "<p>Evaluate the following limit</p>\n<p style=\"padding-left: 30px;\">\\(\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{x^2-\\simplify{{a}+{b}}x+\\simplify{{a}*{b}}}\\)</p>\n<pre class=\"lang-tex prettyprint prettyprinted\"></pre>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "a<b"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..8#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(6..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "<p>Evaluate a limit</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}