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Recall the approximation of ex is:

$$\Large e^x = 1 + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + ...$$

Convert this program that computes ex to now use a function to compute n! as well as xn

You will write the function <tt>int fact(int n)</tt> that computes and returns n!

We have started you with the code to compute an approximation of ex for a single value of <tt>x</tt>. Modify it to now produce the desired output.
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Copied from problem cpp/nestedloops/etox-range (author: redekopp@usc.edu)
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Correct answer
Template / Reference solution

Template / Reference solution

#include <iostream>
#include <cmath>
using namespace std;

// prototype
int fact(int n);

// definition
int fact(int n)
{
\[
int res = 1.0;
for(int i=2; i <= n; i++){
res *= i;
}
return res;
]\
}
int main()
{
double x;
cin >> x;
double etox = 1;
\[
for(int i = 1; i < 10; i++){
etox += pow(x,i)/fact(i);
}
\show:
double x_to_n = 1;
int fact = 1;
for(int i = 1; i < 10; i++){
x_to_n *= x;
fact *= i;
etox += x_to_n / fact;
}
]\
cout << etox << endl;

}
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to just run once with no input use [{}]

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{"stdin": "1.0", "args": ""},
{"stdin": "0.5", "args": ""},
{"stdin": "2.2", "args": ""}
]

C++ test suite
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Property	Value
Description html markup shown to student	<p>Recall the approximation of e<sup>x</sup> is:</p> $$\Large e^x = 1 + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + ...$$ <p>Convert this program that computes e<sup>x</sup> to now use a function to compute <em>n!</em> as well as <em>x<sup>n</sup></em></p> <p>You will write the function <tt>int fact(int n)</tt> that computes and returns <em>n!</em></p> <p>We have started you with the code to compute an approximation of e<sup>x</sup> for a single value of <tt>x</tt>. Modify it to now produce the desired output.</p>
Epilogue html markup shown when solved	remove
Public permissions	remove
Remarks Comments, history, license, etc.	Copied from problem cpp/nestedloops/etox-range (author: redekopp@usc.edu) Copied from problem cpp/for/sum-mult-2-5 (author: redekopp@usc.edu) Copied from problem cpp/for/blastoff (author: redekopp@usc.edu) Copied from problem cpp/while/blastoff (author: redekopp@usc.edu) Copied from problem cpp/while/goldilocks (author: redekopp@usc.edu) Copied from problem cpp/while/sum50 (author: redekopp@usc.edu) Copied from problem cpp/conditionals/rps (author: redekopp@usc.edu) Copied from problem cpp/conditionals/taxbrackets (author: redekopp@usc.edu) Copied from problem cpp/conditionals/nestedec (author: redekopp@usc.edu) Copied from problem cpp/conditionals/extracredit (author: redekopp@usc.edu) Copied from problem cpp/control/flag (author: daveagp@gmail.com) remove
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Choices json list of string, bool pairs e.g. `[["good", true], ["bad", false]]`
Correct answer
Template / Reference solution
Template / Reference solution	#include <iostream> #include <cmath> using namespace std; // prototype int fact(int n); // definition int fact(int n) { \[ int res = 1.0; for(int i=2; i <= n; i++){ res = i; } return res; ]\ } int main() { double x; cin >> x; double etox = 1; \[ for(int i = 1; i < 10; i++){ etox += pow(x,i)/fact(i); } \show: double x_to_n = 1; int fact = 1; for(int i = 1; i < 10; i++){ x_to_n = x; fact *= i; etox += x_to_n / fact; } ]\ cout << etox << endl; }
Java test suite See manual
C++ test suite json list of stdin/args tests e.g. `[{"stdin":"hi", "args":["4", "5"]}, {"stdin":"noargs"}]` to just run once with no input use `[{}]`	[ {"stdin": "1.0", "args": ""}, {"stdin": "0.5", "args": ""}, {"stdin": "2.2", "args": ""} ]
C++ test suite See manual
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Is example? i.e., just a demo	remove
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