Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim_n rightarrow infinity|R_n(x)| = 0 for tor all x in the interval of convergence. f(x) = e^-x, a = 0 First find a formula for f^n(x). f^n(x) = (Type an exact answer.) Next, write the formula for the remainder. R_n(x) = /(n+1)!^n+1, for some value c between x and 0 (Type exact answers.) Find a bound for |R_n(x)| that does not depend on c, and thus holds for all n, Choose the correct answer below. A. |R_n(x)| greaterthanorequalto 1/(n+1)!(x-theta)^n+1 B. |R_n(x) lessthanorequalto e|x|/(n+1)! |x|^n+1 C. |R_n(X)| lessthanorequalto 1/(n+1)! (x-e)^n+1 D. |R_n(X)| lessthanorequalto e^x/(n+1)! x^n+1 E. |R_n(X)| greaterthanorequalto e^|x|/(n+1)! |x|^n+1 F. |R_n(x) greaterthanorequalto e^-x/(N+1)!|x-e
