Estimating remainders Find the remainder term Rn(x)far the Taylor series centered at 0 for the following functions. Find an upper bound for the magnitude of the remainder on the given interval for the given value of n. (The bound is not unique.)f(x) = ex; bound R3 (x) for |x|<1.
Solution 12REStep 1:Given thatf(x) = ex; bound R3 (x) for |x|<1.Step2:To find Find the remainder term Rn(x)far the Taylor series centered at 0 for the following functions. Find an upper bound for the magnitude of the remainder on the given interval for the given value of n.Step3:We know that the remainder in the taylor series expansion of the function f(x) centered at a is Here c is between a and xFrom above, remainder in the taylor series expansion of given function at center a=0 and Hence,
