58. The series x² sec x = 1 + 277 x8 + x6 + 8064 61 720 converges to sec x for –Ħ/2 < x < ™/2. a. Find the first five terms of a power series for the function In sec x + tan x|. For what values of x should the series converge? b. Find the first four terms of a series for sec x tan x. For what values of x should the series converge?

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

Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (8x²) to evaluate the integral 0.65 [065 sin (8x²) dx. Your answer will be an infinite series. Use the first two terms to estimate its value. Enter a mathematical expression [more..]