// Numbas version: exam_results_page_options
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If a limit does not exist, type <code>DNE</code> into the box.</p>", "advice": "<p>$f(x)=\\begin{cases}\\var{case1}\\quad &amp; x&lt;\\var{a}\\\\\\var{case2}\\quad &amp; x=\\var{a}\\\\\\var{case3}\\quad &amp; x&gt;\\var{a}\\end{cases}$</p>\n<p>{diagram}</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"case1": {"name": "case1", "group": "Ungrouped variables", "definition": "fns[0]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}, "case3": {"name": "case3", "group": "Ungrouped variables", "definition": "fns[1]", "description": "", "templateType": "anything", "can_override": false}, "case2": {"name": "case2", "group": "Ungrouped variables", "definition": "expression(string(consts[2]))", "description": "", "templateType": "anything", "can_override": false}, "consts": {"name": "consts", "group": "Ungrouped variables", "definition": "[random(-2..2 except 0),random(1..10),random(1..10),random(1..10)]", "description": "", "templateType": "anything", "can_override": false}, "fns": {"name": "fns", "group": "Ungrouped variables", "definition": "shuffle([expression(string(consts[0])+\"x+\"+string(consts[1])),\n  expression(string(consts[3]))])", "description": "", "templateType": "anything", "can_override": false}, "diagram": {"name": "diagram", "group": "Ungrouped variables", "definition": "jsxgraph(\n  500,500,\n  [-10, 20, 10,-20],\n  [\n    ['functiongraph',[case1,-10,a]],\n    ['functiongraph',[case3,a,10]],\n    ['point', [a, case1endpoint],[strokeColor: 'blue', fillColor: 'white']+[face:'o', size:1]+[name:'']],\n    ['point', [a, case3endpoint],[strokeColor: 'blue', fillColor: 'white']+[face:'o', size:1]+[name:'']],\n    ['point', [a, case2],[strokeColor: 'blue', fillColor: 'blue']+[face:'o', size:2]+[name:'']]\n  ]\n)  ", "description": "", "templateType": "anything", "can_override": false}, "case1endpoint": {"name": "case1endpoint", "group": "Ungrouped variables", "definition": "eval(case1,[\"x\":a])", "description": "", "templateType": "anything", "can_override": false}, "case3endpoint": {"name": "case3endpoint", "group": "Ungrouped variables", "definition": "eval(case3,[\"x\":a])", "description": "", "templateType": "anything", "can_override": false}, "y_of_am1": {"name": "y_of_am1", "group": "Ungrouped variables", "definition": "eval(case1,[\"x\":am1])", "description": "", "templateType": "anything", "can_override": false}, "am1": {"name": "am1", "group": "Ungrouped variables", "definition": "a-1", "description": "", "templateType": "anything", "can_override": false}, "lim": {"name": "lim", "group": "Ungrouped variables", "definition": "expression(if(case1endpoint=case2 and case3endpoint=case2,string(case2),\"DNE\"))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "case1", "case2", "case3", "consts", "fns", "diagram", "case1endpoint", "case3endpoint", "am1", "y_of_am1", "lim"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find $\\lim\\limits_{x\\to \\var{am1} ^+}f(x)$</p>", "answer": "{y_of_am1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, 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