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) = sin x; bound R3(x) for |x|<π.

Solution 13RE

Step 1:

Given that

f(x) = sin x; bound R3(x) for |x|<π.

Step 2</p>

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.