Recall that e :Ln for all x ER n: 0 (1.) Find the Maclaurin series for xe * (2.) Use the 2nd de gree Maclaurin poly nomial for xe* to approvi mate the value of -8.02 eo.02

5)Neat handwriting. Circle the answer. Show work

Evaluate by series approximation

Only handwritten otherwise skip and correct please

Use the equation = 2 x" for |x| < 1 to expand the function in a power series with center c = -7. %3D n=0 (Use symbolic notation and fractions where needed.) 00 Σ n=0 Determine the interval of convergence. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, ). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closcd. Enter DNE if interval is empty.) XE

Find the Maclaurin series for: What is the coefficient next to x^5

I- Find e, and Ea of sin (x) for x = 2 with 1-8 terms of the series. (-1)* sin(z)- 2k +1)! (2k + 1)!" 2. Write a program to find e and &a for Maclaurin series of e* with x 0.5. Then, plot &, and Ea with the terms.

Expand the function s in a power series E a,x" with center e = 0. Find anx". n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anx" Determine the interval of convergence. (Give your answers as intervals in the form (*, *). Use symbol co for infinity, U for combining intervals, and appropriate type of parenthesis " (", ")","[" or "] " depending on whether the interval is open or closed. Enter DNE if interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E

use series t Find 2-4 x 2.

= cosx to find first four terms Use the Maclaurin Series for w(x) = e*and q(x) for nonzero f (x) = w(x) · q(x) Write down the first four terms in the binomial series for (1 + 5x)-4