Weekly Assignment 10

MAT 229, Spring 2021

Instructions:  Show your work!

Let f(x)=(((Underoverscript[Σ, (n=1), ∞])(-1))^(n+1))((((x-2))^n)/((2^n)n))

What is the domain of f(x)? In other words, what is the interval of convergence for the power series?

Approximate (∫_2^4)f(x)d x with error less than 0.0001.

Let g(x)=(((Underoverscript[Σ, (n=0), ∞])(-1))^n)((((x-π))^(2n))/((2n)!))

What is the domain of g(x)? In other words, what is the interval of convergence for the power series?

Find a power series representation for g'(x).

Let h(x)=x ln(1+x)

Using geometric series, what is a power series representation for h(x) centered at 0?

Using the power series representation, approximate (∫_0^1)h(x)d x with error less than 0.0001.