Evaluate the integral ∫ 0
2
​
x
​
1
​
dx or show that it diverges. b) Determine the values of x∈R for which the following power series converges ∑ n=0
[infinity]
​
n!
n 2
(x−2) n
​
c) Find the third degree Taylor polynomial for f(x)=6logx about x=1. Use this Taylor polynomial to to estimate 6log(0.9). d) Calculate the limit lim x→0
​
sinx
e x
−e −x
​
. Provide all working.