2. (a) Find the Maclaurin series of 2/3+x^5 from the Maclaurin series for 1/1 - x and power series operations.   (b)  Use part (a) to calculate the definitie integral 1∫0 2/3+x^5dx. Please note the integral bounds are 1 and 0.

Obtain the power series representation of the ff: 1. 1/(3+x) 2. ln (2-x^2) 3. 2x/(1+x^2) 4. x/(x^2+16)

What is the 7th term in the Taylor series for f(x) = 5e5* taken about x 7th term = 7-6-5-4-3-2-1-36 - 4?

Differentiate the Maclaurin series for 1/(1-2x) twice to find the Maclaurin series of f(x) = 1/(1-2x)^3.

Find Taylor series generated by f(x) = 3x5 - x* + 2x³ + x? - 2, at a =-1 %3D

Find the first 7 terms for the Taylor Series at 0 f(x)=(1)/sqrt(1+x)   Make a substitution in the above taylore series to get the first 7 terms for the Taylor Series f(x)=(1)/sqrt(1-x)

Integrate the series for 1/(1+x) to find the power series for the function ln(1+x).

Find the Maclaurin series of F(x)= x/(1-7x)^2

Use power series operations to find the Taylor series at x = 0 for thefunctions 1/(1 - x)2

The function f(z) = 3 z ln(1 + 2x) is represented as a power series Find the following coefficients in the power series centered at zero: help (numbers) help (numbers) ao 8 = -2 a1 = a2= a3 = -2 83 help (numbers) 00 f(z) = Σan 2". n-0 help (numbers)