Question

Consider the following function.
f(x) = e^(2 x^2), a = 0, n = 3, 0 <= x <= 0.1

(a) Approximate f by a Taylor polynomial with degree n at the number a.
T(3)(x) = ?

(b) Use Taylor's Inequality to estimate the accuracy of the approximation f ≈ Tn(x) when x lies in the given interval. (Round the answer to five decimal places.)
|R(3)(x)| </ ?

Note: Please make sure to answer both a & b

Answer 1

With a=0, this is just a MacLaurin series, so
f(0) = 1
f'(0) = 0
f"(0) = 4
f^⁽³⁾(0) = 48
Now you can write the series and apply the inequality.

Answer 2

thats wrong a) is 1+2x^2 I need help with the answering b if you don't mind