Given the integral sin(x²) dx is difficult to integrate by hand, find a power series for sin(x²) By re-using the power series for sin(x) you already found in a previous homework. Then, integrate term by term to reach a 4-decimal place accuracy. How many terms will you need?

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A: To find the MacLaurin series for a function f(x), use the following formulae. fx=∑k=0∞fk0k!xk Where…

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Q: Suppose you want to approximate sin x with the sixth-order Maclaurin series: х3 х5 х7 + 5! sin x = x…

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A: Using power series we approximate the given integral

Q: 1. Using a Maclaurin series, evaluate the integral shown below to an accuracy of 0.0001: sin x – x…

A: To evaluate , I = ∫01sinx - xx2dx

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A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

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Q: .5 Problem 3. Using series, evaluate the integral x sin(æ³) to 8 decimal places of accuracy

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Q: Calculate sin(+0.06) to within 0.0001 (i.e. the size of the error must be less than 0.0001) by using…

A: Calculate sinπ4+0.06 to within 0.0001 by using the Taylor series about c=π4.

Q: 3. Does the sine series 1 sin (nA x) n=1 converge in the mean-square sense to a function f e L²(0,…

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Q: Find approximate value by using power series to three decimal places. 0.2 1 dx |

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Q: tan"x dxwith an error of magnitude no greater Use the series to estimate the integral than 10

A: The Maclaurin series for tan-1x is given by the formula: tan-1x=∑n=0∞-1nx2n+12n+1 Hence, the given…

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A: Given, ∫00.74sin7x2dx We know that, sinx=x-x33!+x55!-... Therefore,…

Q: Write the first 4 nonzero terms of the integral I= x sin(x)dx using the Maclaurin series for sin(y).

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Q: For which value(s) of k>o will the series converge Σ Σ sin(- n =1

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A: The Maclaurin expansion of sin x is given by  sin x=x-x33!+x55!-x77!+... We have the value of x is…

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Q: Find a Maclaurin series for the given function. 10. f(x) = sin ()

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Q: The integeral S 0 S cos tdt for x = 0.9 is approximately equal to 0 (Type an integer or a decimal.)…

A: Given: ∫0xcost2dt To find: The value of integral given integral when x=0.9 using appropriate series.

Q: Find the Maclaurin series for the functions sin(x/2)

A: Let the function is:                                        fx=sinx2 Concept used: Maclaurin series…

Q: 0.3 11. Use appropriate series to estimate SIn |In(1 + x') dx to 6 decimal place accuracy

A: The estimated value of the given integral upto 6 decimal place accuracy is 0.002009