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 Jun 01, 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 on 3 Feb 2023

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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Problem 55775. Taylor Series

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