// Numbas version: finer_feedback_settings
{"name": "Find the limit of an algebraic fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>Note that on putting $x=\\var{a}$ into $\\displaystyle \\simplify{(x + { -a}) / (x ^ 2 + { -a -b} * x + {a * b}) }$ we get a $0/0$ case and so we have to do more work.</p>\n<p>You can factorise $\\simplify{x ^ 2 + { -a -b} * x + {a * b}}$ and then see what happens.&nbsp;</p>", "variable_groups": [], "showQuestionGroupNames": false, "ungrouped_variables": ["a", "b"], "tags": ["checked2015", "MAS2224"], "variablesTest": {"condition": "", "maxRuns": 100}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "type": "question", "statement": "<p>Find the limit of the following function.</p>", "preamble": {"js": "", "css": ""}, "functions": {}, "parts": [{"marks": 0, "scripts": {}, "prompt": "<p>$\\displaystyle \\simplify{Limit((x + { -a}) / (x ^ 2 + { -a -b} * x + {a * b}),x,{a}) }=\\;$[[0]]&nbsp;(input as a fraction or as an integer).</p>", "gaps": [{"scripts": {}, "answer": "1/{(a-b)}", "showpreview": true, "answersimplification": "all", "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "vsetrange": [0, 1], "checkvariablenames": false, "marks": 2, "checkingaccuracy": 0.001, "notallowed": {"showStrings": false, "message": "<p>Input as a fraction or an integer.</p>", "strings": ["."], "partialCredit": 0}, "expectedvariablenames": [], "checkingtype": "absdiff"}], "showCorrectAnswer": true, "type": "gapfill"}], "rulesets": {}, "variables": {"b": {"templateType": "anything", "definition": "random(1..9 except a)", "description": "", "group": "Ungrouped variables", "name": "b"}, "a": {"templateType": "anything", "definition": "random(-9..9 except 0)", "description": "", "group": "Ungrouped variables", "name": "a"}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Find the limit of an algebraic fraction", "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/"}]}