// Numbas version: finer_feedback_settings
{"name": "Laplace of e^(at)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "name": "Laplace of e^(at)", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>(a) Using the tables, &nbsp;$L[e^{\\var{a}t}]=\\frac{1}{s-\\var{a}}$</p>\n<p>(b)&nbsp;Using the tables, &nbsp;$L[e^{\\var{b}t}]=\\frac{1}{s-(\\var{b})}$</p>\n<p>(c)&nbsp;Using the tables, &nbsp;$L[e^{\\var{c}t}+e^{\\var{d}t}]=\\frac{1}{s-(\\var{c})}+\\frac{1}{s-\\var{d}}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find the laplace transform of $e^{\\var{a}t}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$</p>\n<p>$L\\{e^{at}\\}=\\frac{1}{s-a}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find the laplace transform of $e^{\\var{b}t}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$</p>\n<p>$L\\{e^{at}\\}=\\frac{1}{s-a}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{b})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find the laplace transform of $ { e^{ \\var{c} t}+e^{ \\var{d} t} }$</p>\n<p></p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>When you have the Laplace transform of two functions added together you just get the Laplace transform of each function and add the two answers.</p>\n<p>$L\\{f(t)+g(t)\\}=L\\{f(t)\\}+L\\{g(t)\\}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{c})+1/(s-{d})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "extensions": [], "statement": "<p>You may use a table of Laplace transforms in order to answer the following questions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random (2..9 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random (-9..-2 except [0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random (-9..-2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random (-9..9 except [0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Laplace transform of e^{at}</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}