Find the nth Taylor polynomial for the function, centered at c. f(x) = x^2 * cos x  , n = 2   , c = π

Find the Taylor polynomial T3 (x) for e^3x centered at 0. What is T3 (1)?  (T3 is suppose to look like the image I posted below but i didn't know how to type it.)

"Let T_2(x) be the Taylor polynomial of f(x)=\sqrt(x) centered at a=4. Apply the Error Bound to find the maximum value of the error if we approximate \sqrt(x) with T_2(x) for x in [3.9,4]."

Please give me answers in 5min I will give you like sure

Two waves on a string are given by the following functions: yı (x, 1) = 4 cos(201 – 30x) (cm) y2(x, 1) = -4 cos(201 + 30x) (cm) where x is in centimeters. The waves are said to interfere constructively when their superposition lys| = ly1 + y2|maximum, and they interfere destructively when lys| is a minimum. (a) What are the directions of propagation of waves y1 (x.f) and y2(x, t1)? (b) At t = (= (T/50) s, at what x location y do the two waves interfere constructively, and what is the corresponding value of ys|? (c) At t = (7/50) s, at what locationx do the two waves interfere destructively, and what is the corresponding value of lys?

Consider three real numbers a < c < b and a function f : (a, b) → R such that the (n + 1)-th derivative f(n+1) exists on (a,b) and is continuous. Let Pn denote the Taylor polynomial of order n of f around c  i.e. Would you mind showing me the detail, please. Thank you so much

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