Problem 55775. Taylor Series

Created by Renee Coetsee

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You can use a Taylor series to approximate common functions. The Taylor series for sin(x) is </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\sin(x) = \\sum_{n=0}^{\\infty}\\frac{(-1)^nx^{2n+1}}{(2n+1)!} = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\dots</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Using only the first several terms in the series could get you a good approximation to the function. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 157px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 78.5px; transform-origin: 407px 78.5px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">You can use a Taylor series to approximate common functions. The Taylor series for sin(x) is </span></span></div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img 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" width="294.5" height="46" style="width: 294.5px; height: 46px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Using only the first several terms in the series could get you a good approximation to the function. </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Write a function that takes a point x at which to evaluate the sine function and a tolerance level that defines how close you want the Taylor series approximation to be to the actual value. Your function should output the approximate value of sin(x).</span></span></div></div></div>

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Last Solution submitted on Feb 03, 2023

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Rafael S.T. Vieira on 30 Oct 2022

Using sin(x) to test the tolerance level is probably inadequate. We should be testing how much a new term improved the solution compared to the previous one. If we calculate sin(x) there is no need to use the Taylor series.

Ricardo 12 hours and 24 minutes ago

You are right. I made a solution with the remainder of Lagrange for error estimation. I avoided the sin(x) usage for comparing approximation and real values.

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Solution 9513323

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Cailean MacLabhruinn on 5 Dec 2022

And where is the Taylor series in your solution?

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Problem 55775. Taylor Series

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