11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this series to find the Taylor series at 0 for cos(x³). Write out at least the first six terms of the series. (b) Evaluate cos (x°) dx exactly, using the series in part (a). (c) Approximate the value of cos (x) dx using the first five terms in your answer to (b), and find a bound on the amount of error this involves.

Q: 8. Find the Taylor series of f(x) = sin(x4) about x = 0. = 9. Using the first five terms of the…

A: 8. We have to find the Taylor series of fx=sinx4 about x=0. 9. Using the Taylor series to calculate…

Q: (b) Expand f(x) = x as a sine series in the half interval (0, L). Sketch the series you have found…

A: To expand  f(x) = x  as a sine series in the half-interval (0, L), we can use the standard technique…

Q: 1. Find the Taylor Series for the function f(x) = e centered at a = In 2. Please do not use a known…

A: fx=ex Find the Taylor series for the function centered at a=ln2

Q: The Taylor series for f(x) = e" at a = 4 is ся (х — 4)". Find the first few coefficients. Co C2 C3 =…

A: Given that taylor series of fx=ex at  a=4 is ∑n=0∞ cnx-4nfind the first few…

Q: For f(x) = 4 on (0,t), find the Fourier sine series of f(x). Make sure to write the series.

A:

Q: 8. Determine the Taylor series for f(x) = sin x at x = T. Write in sigma notation. 8b. Estimate…

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Q: (b) Use the first four terms of a power series you found in part (a) to approximate the value of |…

A: The answer is found in step-2

Q: Find the first five terms of the Taylor series for the function f(æ) = In(x) about the point a…

A: The given function is fx=lnx about the point a = 8. Note  that, the Taylor series expansion of f(x)…

Q: Find the power series of the function f(z) = sin(2z) with centre 7/3. Find the power series of the…

A: We will use taylor series at x=a The Taylor series of a real or complex-valued function f (x) that…

Q: a. Series for sinh lx Find the first four nonzero terms of the Taylor series for sinh x = dt V1 + f°…

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Q: Please help me with these questions. I am having a hard time understanding what to do. For the first…

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Q: Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b)…

A:

Q: Find taylor series/polynomial

A: Required Taylor series : f(x)=1−2!25x4​+4!625x8​−6!15625x12​+⋯Explanation:The Taylor series…