Find the taylor polynomial of degree n approximating the

Question

1. Write a general term for the sequence, if one exists, assuming a domain starting with n = 1.

3, 8, 15, 24, 35, 48....

2. compute the sums indicated.

_i=1∑⁵ (i+1)/(i²+i)

3. find the sum if the series converges.

_n=0∑^∞ 2n/(n+2)

4. Find the Taylor polynomial of degree n approximating the given function near x = 0. Using a graphing utility, sketch the given function and the Taylor approximation on the same coordinate system.

y = 1/√1+x, n=3

y= x ln(x+1), n=3

5. find the Taylor polynomial of degree n near x = a for the given n and a.

y = sinx, a= Π, n=5

y = x^1/3, a= 1, n=4

 

 

 

5. find the Taylor series polynomial of degree at least four which is a solution of the boundary value problem.

f'(x)= (1+xy), f(0)=1.