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Expert-verified Found in: Page 692 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # In Exercises 23–32 we ask you to give Lagrange’s form for the corresponding remainder, ${R}_{4}\left(x\right)$${e}^{x}$

The required answer is ${R}_{4}\left(x\right)=\frac{{e}^{c}}{120}{x}^{5}$

See the step by step solution

## Step 1. Given Information

The given function is $f\left(x\right)={e}^{x}$

## Step 2. Explanation

The lagrange form for the remainder ${R}_{4}\left(x\right)\mathrm{is}{R}_{4}\left(x\right)=\frac{{f}^{5}\left(c\right)}{5!}{x}^{5}$

Now, we will evaluate the fifth derivative of the function $f\left(x\right)={e}^{x}\mathrm{which}\mathrm{is}{e}^{x}$

Thus, we get,

${R}_{4}\left(x\right)=\frac{{e}^{c}}{5!}{x}^{5}\phantom{\rule{0ex}{0ex}}{R}_{4}\left(x\right)=\frac{{e}^{c}}{120}{x}^{5}$ ### Want to see more solutions like these? 