Homework Answers
CODE
import math
def mysin(x):
sum = 0
term = 1
i = 0
while(term > 10**(-6)):
term = x**(2*i+1)/math.factorial(2*i+1)
if i % 2 == 1:
sum -= term
else:
sum += term
i += 1
return sum
print(mysin(2))
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This is the given code: /** * This program uses a Taylor Series to compute a...
This is the given code:
/**
* This program uses a Taylor Series to compute a value
* of sine.
*
*/
#include<stdlib.h>
#include<stdio.h>
#include<math.h>
/**
* A function to compute the factorial function, n!.
*/
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}
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}
int main(int argc, char **argv) {
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fprintf(stderr, "Usage: %s x n ", argv[0]);
exit(1);
}
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int...
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A. Write a function script called cos_series
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Hint: try a “for loop” and set “format long” in
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a.) Write a C++ program that calculates the value of the series
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example, if n= 5, the program should calculate the sum of 5 terms
in the series for a given values of x. The program should use
switch statements to determine the choice sin x AND cos x, sin...
Problem1. Write a C program, called cos.approx.c, that computes the approximate value of cos(x) according to its Tavlor series expansion: (-1)"r2n (2n)! x2 x4x6x8x10 cos(x)-Σ 1 This series produces the exact value of cos(x) for any real number x, but contains an infinite number of terms. Obviously, a computer program can compute only a finite number of terms. Thus, you will have to truncate the infinite series in (1). Your program should be able to do so in two different...
The cosine function can be evaluated by the following infinite series as (where the angle x is given in radians) cos x =1--+ + 2! 4! 6! Create a second function M-file mycos that takes the angle x (in radians), and returns cos(x) with an absolute iterative error less than 1.0e-18. Test your function to find cosine of ?/2 and 2? Display the Expansion order, and the actual error (absolute error, not the relative one) and iterative error using fprintf...
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This is the given code:
/**
* This program uses a Taylor Series to compute a value
* of sine.
*
*/
#include<stdlib.h>
#include<stdio.h>
#include<math.h>
/**
* A function to compute the factorial function, n!.
*/
long factorial(int n) {
long result = 1, i;
for(i=2; i<=n; i++) {
result *= i;
}
return result;
}
int main(int argc, char **argv) {
if(argc != 3) {
fprintf(stderr, "Usage: %s x n ", argv[0]);
exit(1);
}
double x = atof(argv[1]);
int...
Use in MATLab
(b) Write a computer program to calculate ex as an approximate series summation, to an accuracy of 1010. The value of x should be supplied to the program with the "input" command. Do not run the program.
(b) Write a computer program to calculate ex as an approximate series summation, to an accuracy of 1010. The value of x should be supplied to the program with the "input" command. Do not run the program.
Convince yourself that the Maclaurin Series for cos(x) is:
A. Write a function script called cos_series
that takes that takes as its inputs, x and N and has output given
by the sum in the N-term Maclaurin Series approximation for Cos(x).
Hint: try a “for loop” and set “format long” in
your code. You may use the MATLAB built-in function factorial()
B. Check your code by finding the 2-terms,
3-terms, 4-terms, 5-terms and 6-terms Maclaurin Series
approximations every 30 degrees...
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