Use a well known series to answer the following. (a) Find the first four nonzero terms of the Taylor series about 0 for f(z) = _4 . . Simplify all coefficients. f ( z ) = - + (b) Find f(8)(0) = 4. [-/3 Points] DETAILS MY NOTES Using a known series, find the first four nonzero terms of the Taylor series about 0 for 25 . Simplify all coefficients. 925 + 5. [-/3 Points] DETAILS MY NOTES Using a known series, find the first three nonzero terms of the Taylor series about 0 for tsin(t2) - 3 . Simplify all coefficients. tsin(t2) - +3 = +6. [-/3 Points] Expand the quantity about 0 in terms of the variable %. Assume P is large in comparison to x. Write out the rst 4 nonzero terms. Use upper case P. \\/P+x= + 7. [/3 Points] Expand the quantity about 0 in terms of the variable %. Assume a is large in comparison to r. Write out the first 4 nonzero terms. 4: (a +r)2 8. [-/5 Points] Find the first three nonzero terms of the Taylor series for for) = (-2"3 around 0. e\": + Use this information to approximate the integral. (Round your answer to three decimal places.) 1 lexadx z 8. [-/5 Points] DETAILS MY NOTES Find the first three nonzero terms of the Taylor series for f(x) = ex around 0. ex3 + Use this information to approximate the integral. (Round your answer to three decimal places.) 9. [-/3 Points] DETAILS MY NOTES Find the exact sum of _pyp - 1 for ly|