Homework Answers
%%%%Matlab code
clc;
close all;
clear all;
x=input('Enter the x : ');
N=input('Enter the number of term ;');
sum=0;
for n=1:N
sum=sum+(-1)^(n+1)*x^n/n;
end
fprintf('ln(1+%1.2f)=%f \n',x,sum);
OUTPUT:
Enter the x : 0.4
Enter the number of term ;10
ln(1+0.40)=0.336469
Add Answer to:
Problem #5 Equation 1 is the infinite Taylor series expansion of ln(1 + x), where In...
Problem #5 Equation 1 is the infinite Taylor series expansion of ln(1 + x), where In is the natur...
Problem #5 Equation 1 is the infinite Taylor series expansion of ln(1 + x), where In is the natural logarithm: 5 (-1)k+1 Eqn. 1 Σ(-1)k+1 k In(1 + x) Eqn. 2 Equation 2 is the finite version that calculates an approximation for ln(1 + x). Instead of letting k go to infinity, it stops summing once k reaches some fixed value N. Task Develop a program that can compute ln(1 +x). Have it first ask the user to enter x...
Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor'...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
Problem 5 xx The Taylor series expansion for sin(x) is sin(x) = x -H + E-E+...
Problem 5 xx The Taylor series expansion for sin(x) is sin(x) = x -H + E-E+ = o E- (-1) . 2n +1 no (2n+1)! !57 where x is in radians. Write a MATLAB program that determines sin(x) using the Taylor series expansion. The program asks the user to type a value for an angle in degrees. Then the program uses a while loop for adding the terms of the Taylor series. If an n is the nth term in...
(1 point) Find Taylor series of function f(x) = ln(x) at a = 7. (f(1) =...
(1 point) Find Taylor series of function f(x) = ln(x) at a = 7. (f(1) = (x – 7)") ܫ)ܐܶ Co C1 C2 = C3 = C4 Find the interval of convergence. The series is convergent: from 2 = left end included (Y,N): to = right end included (YN):
Use this list of Basic Taylor Series to find the Taylor Series for tan-1(x) based at...
Use this list of Basic Taylor Series to find the Taylor Series for tan-1(x) based at 0. Give your answer using summation notation, write out the first three non-zero terms, and give the interval on which the series converges. (if you need to enter 00, use the 00 button in CalcPad or type "infinity" in all lower-case.) The Taylor series for tan -1(x) is: The first three non-zero terms are: + + +
The Taylor series converges to tan-1(x) for...
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!.
*/
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...
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9...
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9 (-1)"+(v - 1) n=1 for y-1€ (-1,1] (that is, y E (0,2]). What polynomials do we get if we truncate this series at n = 1? n = 2? n = 0 (hint: the n = Oth approximation is defined!)? Compare the value of each of these with that of In(y) at y = 1.1 and y = 1.75. Note how the error differs...
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+...
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...
If f(x) has the following Taylor series, Σ 5" (x + 2)", (n + 1)(n+2) P=0...
If f(x) has the following Taylor series, Σ 5" (x + 2)", (n + 1)(n+2) P=0 find the value of f(2)(-2).
pset3: Problem 1 Up Next Prev of c such that the area of the region bounded by the parabolae y - 2-2 and y (1 pt) Find the value(e) 4608. Answer (separate by commas): cI pset10: Problem 2 Pr...
pset3: Problem 1 Up Next Prev of c such that the area of the region bounded by the parabolae y - 2-2 and y (1 pt) Find the value(e) 4608. Answer (separate by commas): cI pset10: Problem 2 Prev UpNext (1 pt) The Taylor series for f (x) = ln (sec(x)) at a = 0 is Σ.:0 cn x". Find the following coefficients. C2 = Cgー C4= pset6: Problem 1 Prev Up Next (1 pt) Find the infinite sum (if...
Problem #5 Equation 1 is the infinite Taylor series expansion of ln(1 + x), where In is the natural logarithm: 5 (-1)k+1 Eqn. 1 Σ(-1)k+1 k In(1 + x) Eqn. 2 Equation 2 is the finite version that calculates an approximation for ln(1 + x). Instead of letting k go to infinity, it stops summing once k reaches some fixed value N. Task Develop a program that can compute ln(1 +x). Have it first ask the user to enter x...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
Problem 5 xx The Taylor series expansion for sin(x) is sin(x) = x -H + E-E+ = o E- (-1) . 2n +1 no (2n+1)! !57 where x is in radians. Write a MATLAB program that determines sin(x) using the Taylor series expansion. The program asks the user to type a value for an angle in degrees. Then the program uses a while loop for adding the terms of the Taylor series. If an n is the nth term in...
(1 point) Find Taylor series of function f(x) = ln(x) at a = 7. (f(1) = (x – 7)") ܫ)ܐܶ Co C1 C2 = C3 = C4 Find the interval of convergence. The series is convergent: from 2 = left end included (Y,N): to = right end included (YN):
Use this list of Basic Taylor Series to find the Taylor Series for tan-1(x) based at 0. Give your answer using summation notation, write out the first three non-zero terms, and give the interval on which the series converges. (if you need to enter 00, use the 00 button in CalcPad or type "infinity" in all lower-case.) The Taylor series for tan -1(x) is: The first three non-zero terms are: + + +
The Taylor series converges to tan-1(x) for...
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...
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9 (-1)"+(v - 1) n=1 for y-1€ (-1,1] (that is, y E (0,2]). What polynomials do we get if we truncate this series at n = 1? n = 2? n = 0 (hint: the n = Oth approximation is defined!)? Compare the value of each of these with that of In(y) at y = 1.1 and y = 1.75. Note how the error differs...
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...
If f(x) has the following Taylor series, Σ 5" (x + 2)", (n + 1)(n+2) P=0 find the value of f(2)(-2).
pset3: Problem 1 Up Next Prev of c such that the area of the region bounded by the parabolae y - 2-2 and y (1 pt) Find the value(e) 4608. Answer (separate by commas): cI pset10: Problem 2 Prev UpNext (1 pt) The Taylor series for f (x) = ln (sec(x)) at a = 0 is Σ.:0 cn x". Find the following coefficients. C2 = Cgー C4= pset6: Problem 1 Prev Up Next (1 pt) Find the infinite sum (if...
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