Question

Hello, I am having trouble with part c of this question.

Here is my work so far:

The solution for part c states that a possible solution is (e^16 * 4^3) / 3!

I am having trouble understanding how they got e^16 or why they decided to use e^(4^2) for M in the equation |f(x) - Tn(x)| <= (M / (n + 1)!) * |x - 0|^(n + 1).

From my understanding, I have to maximize H^3(x) (i.e. 3rd derivative of H(x)) ; in order to find this, I thought to plug in k = 0 for the H(x) formula in sigma notation. After that, we could use the knowledge that the coefficient of x^3 would equal H^3(x) / 3! ; If you can offer any insight on my error I would appreciate it!

Thank you.

(12 points) Let F(x) be the function fe dt. Let G(x) be the function F(t)dt. Let H(x) SG(t)dt (a) Find the Taylor series for F(r), based at b be the function 0. Write your answer using notation (b) Find T3(r), the third Taylor polynomial of the function G(z) based at b 0. (c) Use Taylor's Inequality to find an upper bound for the error H(x)-T2(x)| on the interval (0,4], where T2(x) is the second Taylor polynomial of H (r), based at b 0 Hix) e Suk \1れ1はオ212ナM7ュし) 0-メ Iul2oo Au Ansur for c Fle Eind T Mx-ot 31 x- 31219 0)

Answer 1

Any query in any step then comment below.. i will help you..

G(x) FCt dt () F(1) ,x2 rom taj ler se n NOv, 1ucri-TC) max 31 (4 2 max 31 Nou, e hmay mum uralue at xY (W3 (ey Frr 16 1