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plement a Taylor series approximation of some mathematical functions. mathematics, the Taylor series is a way of approximating transcendental functions such as sin z or log æ. In this approach, we c proximate a mathematical function as closely as we might want to by adding together numbers that get us closer and closer to ti e value of the function. For example, the exponential function e" can be approximated as: e = 1+x+ 2! +.. 3! d the sin function can be approximated as: (-1)" sin z = a 3! 2 2n+1 (2n + 1)! 5! e more terms we include in our approximation, the better an approximation we get of sin z. In this assignment, you must implem ylor series approximations for these two functions. Your functions should take two parameters: the value of a and the number of use in the approximation: /** * Calculate an approximate value for the exponential function. * eparam the value to raise e to the power of to the .e., * @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 double approxExp(double x, int terms); /** IM:

plement a Taylor series approximation of some mathematical functions. mathematics, the Taylor series is a way of approximating transcendental functions such as sin z or log æ. In this approach, we c proximate a mathematical function as closely as we might want to by adding together numbers that get us closer and closer to ti e value of the function. For example, the exponential function e" can be approximated as: e = 1+x+ 2! +.. 3! d the sin function can be approximated as: (-1)" sin z = a 3! 2 2n+1 (2n + 1)! 5! e more terms we include in our approximation, the better an approximation we get of sin z. In this assignment, you must implem ylor series approximations for these two functions. Your functions should take two parameters: the value of a and the number of use in the approximation: /** * Calculate an approximate value for the exponential function. * eparam the value to raise e to the power of to the .e., * @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 double approxExp(double x, int terms); /** IM:

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Description Implement a Taylor series approximation of some mathematical functions. In mathematics, the Taylor series is a way of approximating transcendental functions such as sin x or log x. In this approach, we can approximate a mathematical function as closely as we might want to by adding together numbers that get us closer and closer to the true value of the function. For example, the exponential function e" can be approximated as: 73 e" = 1+x + 2! 3! - nl and the sin function can be approximated as: (-1)" 73 sin z = x - 3! „5 77 2n+1 (2n + 1)! 5! 7! n=0 The more terms we include in our approximation, the better an approximation we get of sin x. In this assignment, you must implement Taylor series approximations for these two functions. Your functions should take two parameters: the value of x and the number of terms to use in the approximation: /** * Calculate an approximate value for the exponential function. @param the value to raise e to the power of (i.e., e to the x) * @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 */ double approxExp(double x, int terms); /** * Calculate an approximate value for the sine function. * @param the value to calculate the sine of @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 */ double approxSine(double x, int terms); For example, when my test code calls approxExp(2.2, 4), you should return the sum of the first four terms of the e approximation, i.e.: 1+x + 2! (2.2)? = 1+ (2.2) + 2! (2.2)3 = 1+2.2 + 2.42 +1.77467 = 7.394667 3! 3! If my test code calls approxSsin(3.14, 3) , you should return the sum of the first three terms of the sin a approximation, i.e.: 73 (3.14)3 (3.14)5 30.959 305.245 = 3.14 – 5! = 3.14 0.523875 3! 3! 120 6 120
Transcribed Image Text:Description Implement a Taylor series approximation of some mathematical functions. In mathematics, the Taylor series is a way of approximating transcendental functions such as sin x or log x. In this approach, we can approximate a mathematical function as closely as we might want to by adding together numbers that get us closer and closer to the true value of the function. For example, the exponential function e" can be approximated as: 73 e" = 1+x + 2! 3! - nl and the sin function can be approximated as: (-1)" 73 sin z = x - 3! „5 77 2n+1 (2n + 1)! 5! 7! n=0 The more terms we include in our approximation, the better an approximation we get of sin x. In this assignment, you must implement Taylor series approximations for these two functions. Your functions should take two parameters: the value of x and the number of terms to use in the approximation: /** * Calculate an approximate value for the exponential function. @param the value to raise e to the power of (i.e., e to the x) * @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 */ double approxExp(double x, int terms); /** * Calculate an approximate value for the sine function. * @param the value to calculate the sine of @param terms the number of Taylor series terms to use in the approximation @pre terms > 0 */ double approxSine(double x, int terms); For example, when my test code calls approxExp(2.2, 4), you should return the sum of the first four terms of the e approximation, i.e.: 1+x + 2! (2.2)? = 1+ (2.2) + 2! (2.2)3 = 1+2.2 + 2.42 +1.77467 = 7.394667 3! 3! If my test code calls approxSsin(3.14, 3) , you should return the sum of the first three terms of the sin a approximation, i.e.: 73 (3.14)3 (3.14)5 30.959 305.245 = 3.14 – 5! = 3.14 0.523875 3! 3! 120 6 120
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