Please answer all the questions, Thank you :

[answerhappygod]

Please answer all the questions, Thank you :

Please Answer All The Questions Thank You 1 (275.48 KiB) Viewed 10 times

6. (1 point) In this problem you will approximate the value of e Suppose that F(x) is an antiderivative of Taylor series is 0 0.125 -8x e 8x n = ∞ Use your Taylor series to find a series representation of n=1 8x 1 dx = Find this approximation. 0.125 -8x e 1 -8x ∞ Σ dx ≈ n=1 8x 0.125 -8x # 8x · 1 with F(0) = 0. Find the Taylor series for F(x) centered at x = 0. 0.125 -8x What is the smallest value of n so that the nth partial sum of your series is guaranteed to approximate the actual value of the definite integral with an error of less than 10-³? 8x 1 1 dx. dx.

(1 point) In this problem you will approximate the value of Use your Taylor polynomial to approximate 0.1 6.⁰. Find the fourth-order Taylor polynomial of cos √3x centered at x = = 0. P4(x) = cos √3x dx≈ ●●● Error < • 0.1 [... 0 0.1 cos √3x dx. cos √3x dx. Use the alternating series error estimate to bound the error in your approximation.