Chapter 5.10, Problem 49ES

Use a graphing utility to generate the graph of

$y={\left(1+\frac{1}{x}\right)}^{x+1}-{\left(1+\frac{1}{x}\right)}^x$

in the window $\left[0,100\right]\times \left[0,0.2\right]$ , and use that graph and part (d) or Exercise $48$ to make a rough estimate of the error in the approximation

$e\approx {\left(1+\frac{1}{50}\right)}^{50}$