\fFind the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n =4, c= 6 P ( x) =Approximate the function at the given value of X, using the Maclaurin polynomial of degree n = 4. (Round your answer to four decimal places.) f(X) = xzeix 2 3+ix4 P=x 4 2 m4; = I:| X Approximate the function at the given value of x, using the Taylor polynomial of degree n = 3, centered at c = 27. (Round your answer to three decimal places.) rm = R 1127.03) 3 3+i(x27) 1(x 2mm; 27 2187 531,441 |:| P (x 27)3 Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.) (0.5)2 + (0.5)4 21 4! cos(0.5) 1' 1 Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = ex, approximate f(0.9)Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. (Enter your answer using interval notation. Round your answer to four decimal places.) x) =sinxzxX_ 3! Determine the values ofx for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. (Enter your answer using interval notation. Round your answer to four decimal places.) f(x) = e'ZX t 2x + 2X2 1X3 3 State where the power series is centered. 0O (-1)"(x - 41) 8n n = 0 (8n) XFind the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.) Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.) game Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.) (_1)F'i + 1(X _ 6)\" n6\" Ms :1 ll l_. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.) 50 n !X\" n =1 (2n)