## Physics 222/322 Assignment 3

### Directions

Please turn in this assignment (and all future assignments for this course) by emailing them to me . Please use the subject of "Physics 222 HW3" for these assignments (if you use the link above, the subject will be added automatically). Please attach the any source code to programs that you write for this assignment. If you write more than one program, attach each separately. When answering the questions themselves feel free to answer directly in the body of your message (or attach your answers). I may take off points for assignments that are not sent to me in the correct form.

1. #### 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: e1. 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 xy.

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.