(3) (a) Find Taylor polynomial of degree three at x0 = 0, for f(x) = 2x·

How do I estimate the error R(x) when x < 1/2?  Let f(x) = cos(4x), and it is replaced by P(x)=1-(16x 2 /2) an order 2 Taylor polynomial, centered at 0.

Find the degree three Taylor polynomial T3 centered at x = = 0 for f when 2. T3(x) 1. T3(x) = ln 3. 3. T3(x) 4. T3(x) 5. T3(x) f(x) 6. T3(x) = - X 3 = = = = In 3+ 4 3x = In 3 4 -X 3 + ln(3 – 4x). 4 -X 3 x² 4 8 io - X 3 9 22 - 9 + 8 9 64 81 + 8 610 شرح 4 z x + 7 x 64 81 X3 + 64 81 خرج 64 -x³ 81 32 -x³ 81 64 من مخ 81

for b i got 5/4 (3!) is it correct ?

3. Let T,(x)= f(a)+ f '(a)(x-a)+ f"(a) (x-a)² + 2 f'(a) (x-a) be the Taylor polynomial of degree three for the 6 function f(x), centered at the point x=a. a) Find T, '(x), T, "(x), and T,"'(x). b) Evaluate T '(x), T, "(x), and T,"'(x) at x=a to verify that: T;(a) = f(a), T, "(a) = f'(a), T",(a) =f"(a), and T,"'(a) = f"(a). %3D

(3) (a) Find Taylor polynomial of degree three at x0 = 0, for f(x) = = 2-x (b) Give the maximum absolute error bound for −1 ≤ x ≤ 1.

could you pleaae do all parts and could the answer be written out please , not typed up. Thank you