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#### Calculating e

Write a

separate function that uses the expression:e = lim (1 + 1/n)

^{n}n → ∞

to find approximations for the mathematical constant e. Your function should take as input a long double precision number, and return an approximate value for*e*as a long double precision number. Be careful about the types that you use for numbers in this program. Your main program should ask for the user to input a number that you will pass to your function for it to use as*n*in the formula above for calculating*e*. Your program should compare your approximation for*e*to the value that you get by calculating: e^{1}. You can do so using the exp function. Note to use this function, you must have an#include <cmath>

line near the top of your program. To use this function include a line something like:cout << exp(1.0L) << '\n';

This will give exp a long double version of 1.0, which will give you a fairly precise value for*e*. Also, calculate and print out the percent error in your calculation of*e*. Note that you also need to use the pow(x,y) function which calculates x^{y}.Test your program with the following input: 1., 10., 100., 1000., 10.

^{6}, 10.^{9}and 10.^{12}. Send your results in with your assignment. Comment on your results.Use the

*cout.precision(j)*command to force cout to show*j*digits. Use this function before the places where you are going to print out results to force the program to show you enough digits so that you can tell the accuracy of your program. 8 or 10 digits will probably be sufficient.-
#### Answer the following Chapter Review questions from your textbook:

3.7, and 3.8.