Problem 52562. Easy Sequences 6: Coefficient sums of derivatives

Created by Ramon Villamangca

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>Consider the polynomial function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P\\left(x\\right)=5x^3+6x^2-7x-8</w:t></w:r></w:customXml><w:r><w:t> and its first-order derivative </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\frac{dP}{dx}=15x^2+12x-7</w:t></w:r></w:customXml><w:r><w:t>. The sums of the coefficients of P and P', are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>5 + 6 - 7 - 8 = -4</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>15+12-7= 20</w:t></w:r></w:customXml><w:r><w:t>, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>-4,\\ 20,\\ 42, ...</w:t></w:r></w:customXml><w:r><w:t> etc. The total sum of this sequence converge to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>88</w:t></w:r></w:customXml><w:r><w:t>.</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>For this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[5\\ 6\\ -7\\ -8]</w:t></w:r></w:customXml><w:r><w:t>. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.</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: 20.440000534057617px; 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: normal; text-decoration: none; white-space: normal; "><div style="block-size: 191px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 98px; 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; text-align: left; 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; ">Consider the polynomial function <img src="data:image/png;base64,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" width="163" height="20" style="width: 163px; height: 20px;"><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; "> and its first-order derivative <img src="data:image/png;base64,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" width="129.5" height="35" style="width: 129.5px; height: 35px;"><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; ">. The sums of the coefficients of P and P', are <img src="data:image/png;base64,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" width="120" height="18" style="width: 120px; height: 18px;"><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; "> and <img src="data:image/png;base64,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" width="108" height="18" style="width: 108px; height: 18px;"><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; ">, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: <img src="data:image/png;base64,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" width="90" height="18" style="width: 90px; height: 18px;"><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; "> etc. The total sum of this sequence converge to <img src="data:image/png;base64,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" width="18" height="18" style="width: 18px; height: 18px;"><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; ">.</div><div style="block-size: 84px; 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; text-align: left; 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; ">For this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, <img src="data:image/png;base64,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" width="98.5" height="19" style="width: 98.5px; height: 19px;"><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; ">. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.</div></div></div>

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Problem 52562. Easy Sequences 6: Coefficient sums of derivatives

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