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{"name": "Tony's copy of Evaluate a limit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "ungrouped_variables": ["a", "b"], "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>", "preamble": {"js": "", "css": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Evaluate a limit</p>"}, "parts": [{"unitTests": [], "type": "gapfill", "scripts": {}, "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "type": "jme", "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "marks": 1, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "failureRate": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "vsetRangePoints": 5, "answer": "+inf", "checkingAccuracy": 0.001}], "prompt": "<p>Pour des limites infinies, noter soit +inf soit -inf</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "type": "gapfill", "scripts": {}, "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "type": "jme", "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "marks": 1, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "failureRate": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "vsetRangePoints": 5, "answer": "+inf", "checkingAccuracy": 0.001}], "prompt": "\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"unitTests": [], "type": "gapfill", "scripts": {}, "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "gaps": [{"vsetRange": [0, 1], "unitTests": [], "type": "jme", "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "marks": 1, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "failureRate": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "vsetRangePoints": 5, "answer": "-inf", "checkingAccuracy": 0.001}], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "showCorrectAnswer": true}, {"unitTests": [], "type": "gapfill", "scripts": {}, "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "type": "jme", "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "marks": 1, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "failureRate": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "vsetRangePoints": 5, "answer": "+inf", "checkingAccuracy": 0.001}], "prompt": "\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false}], "tags": [], "variable_groups": [], "statement": "<p>D&eacute;terminer les limites suivantes</p>\n<ol>\n<li>&nbsp;\\(\\displaystyle{\\lim_{x \\to +\\infty}}x^2+x+1\\)</li>\n<li>&nbsp;\\(\\displaystyle{\\lim_{x \\to -\\infty}}x^2+x+1\\)</li>\n<li>&nbsp;\\(\\displaystyle{\\lim_{x \\to 0}}e^x+ln(x)\\)</li>\n<li>&nbsp;\\(\\displaystyle{\\lim_{x \\to +\\infty}}\\frac{e^x+ln(x)}{x}\\)</li>\n</ol>\n<p style=\"padding-left: 30px;\"></p>\n<pre class=\"lang-tex prettyprint prettyprinted\"></pre>", "name": "Tony's copy of Evaluate a limit", "variables": {"b": {"group": "Ungrouped variables", "name": "b", "templateType": "randrange", "definition": "random(6..15#1)", "description": ""}, "a": {"group": "Ungrouped variables", "name": "a", "templateType": "randrange", "definition": "random(1..8#1)", "description": ""}}, "variablesTest": {"condition": "a<b", "maxRuns": 100}, "extensions": [], "functions": {}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Tony FEVRIER", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2706/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Tony FEVRIER", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2706/"}]}