// Numbas version: finer_feedback_settings
{"name": "Use algebra to evaluate limit 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Use algebra to evaluate limit 3", "tags": [], "metadata": {"description": "<p>Evaluate $\\displaystyle \\quad \\lim_{x\\to a} \\frac{ax^2+bx+c}{ex+d} \\quad $ algebraically.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Evaluate $\\displaystyle \\quad \\lim_{x\\to a} \\frac{ax^2+bx+c}{ex+d} \\quad $ algebraically.</p>", "advice": "<p></p>\n<p>Factorise the numerator to obtain</p>\n<p>\\[ \\lim_{x\\to \\var{anum}} \\frac{\\simplify{{knum}({x}-{anum})(x+{bnum})}}{\\simplify{(x-{anum})}} =\\lim_{x\\to \\var{anum}} \\var{knum}(\\simplify{x+{bnum}}) =\\simplify{{knum}*( {anum}+{bnum})}\\]</p>", "rulesets": {}, "extensions": [], "variables": {"anum": {"name": "anum", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "<p>a constant</p>", "templateType": "anything"}, "bnum": {"name": "bnum", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "<p>constant b</p>", "templateType": "anything"}, "bma": {"name": "bma", "group": "Ungrouped variables", "definition": "bnum-anum", "description": "<p>bnum - anum</p>", "templateType": "anything"}, "atb": {"name": "atb", "group": "Ungrouped variables", "definition": "anum*bnum", "description": "<p>anum x bnum</p>", "templateType": "anything"}, "knum": {"name": "knum", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>constant k</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["anum", "bnum", "bma", "atb", "knum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Evaluate</p>\n<p>\\[ \\lim_{x\\to \\var{anum}} \\frac{\\simplify{{knum}*x^2+{knum}*{bma}x-{knum}*{atb}} }{\\simplify{x-{anum}}}.\\]</p>\n<p>giving your answer in exact form.&nbsp;</p>\n<p><strong>Answer</strong>:&nbsp;[[0]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{knum}*({anum}+{bnum})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Wan Mekwi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4058/"}]}]}], "contributors": [{"name": "Wan Mekwi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4058/"}]}