// Numbas version: exam_results_page_options
{"name": "W02Q01", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "ungrouped_variables": [], "variables": {}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"description": "<p>Week 2, Question 1</p>", "licence": "None specified"}, "functions": {}, "advice": "<p>$\\frac{d}{dz}e^z = \\frac{d}{dz}(1 + \\frac{z}{1!} + \\frac{z^2}{2!} + \\frac{z^3}{3!} + ...)$</p>\n<p>$= \\frac{d}{dz}1 + \\frac{1}{1!}\\frac{d}{dz}z + \\frac{1}{2!}\\frac{d}{dz}z^2 + \\frac{1}{3!}\\frac{d}{dz}z^3 + ... $</p>\n<p>$= 0 + \\frac{1}{1!} + \\frac{2z}{2!} + \\frac{3z^2}{3!} + ... $</p>\n<p>$= 1 + \\frac{z}{1!} + \\frac{z^2}{2!} + \\dots = e^z$</p>", "extensions": [], "name": "W02Q01", "statement": "<p>The function $e^z$ can be defined by the following power series:</p>\n<p>$e^z = 1 + \\dfrac{z}{1!} + \\dfrac{z^2}{2!} + \\dfrac{z^3}{3!} + \\dots $ </p>\n<p>This power series has the property of being absolutely convergent for any $z$. Thus a rearrangement of its terms is allowed. Show that the following relation holds:</p>\n<p>$\\dfrac{d}{dz}e^z=e^z$</p>", "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"prompt": "<p>No submission required for this task. Try to solve the problem by yourself and click on <em>Reveal answers</em> to compare with the given solution.</p>", "type": "information", "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customName": "", "useCustomName": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": []}], "contributors": [{"name": "Johannes Ba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1898/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}]}]}], "contributors": [{"name": "Johannes Ba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1898/"}, {"name": "Philipp Bucher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2658/"}]}