The natural log of 2, (In 2) can be found using the power series below: In...
Please show exactly how it is in MATLAB The cosine function can be evaluated by the following infinite series: cos ? = 1 − ?^2/ 2! + ?^4/ 4! − ?^6 /6! + ⋯ Create an M-file to compute cos(1.2345 rad) for up to and including eight terms, which is up to the term x^14/14!. a) Your program should compute and display the values of cos ? as each term in the series is added, e.g. cos ? = 1...
Problem 2. Use zero- through fourth-order Taylor series expansions to predict G (0.35) the function considering a base point at ωο-0.25. Compute the true percent relative error (Et) for each approximation. Discuss the meaning of the results. Problem 2. Use zero- through fourth-order Taylor series expansions to predict G (0.35) the function considering a base point at ωο-0.25. Compute the true percent relative error (Et) for each approximation. Discuss the meaning of the results.
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...
2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the composite trapezoidal rule with n = exact value of integral and compute the true percent relative error for this approximation 4. Calculate the (b) How many subintervals would be needed to estimate the integral with the composite trapezoidal rule with an accuracy of 102? (c) Estimate the integral using the composite Simpson's 1/3 rule with n = true percent relative error for this approximation...
Instructions: Submit your script in a file named hwk08.m to the dropbox before 11:59 pm on the due date NOTE: This assignment is neither quick nor simple. You will be well served to start on it early, and to ask for help if you need it. Being a more substantial assignment than earlier hwk, it is worth- s. When you ask your calculator for the value of a function for a specified argument, (e.g., sin(22), cos(74), In(6.5)), it almost certainly...
w Problem Statement: In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Mathematically, the n" number of a mathematical series is defined as follows: T. -Σ . . Write a CH program that: Reads a positive integer k from the user. If the user enters a negative value,...
The function e→ can be approximated by its McLaurin series expansiou as follows (note the alternating and -): 2 2! 3! rT 7l Alternatively, note that e* . Thus, e McLaurin series expansion of e. That is can also be apporximated by 1 over the degree of the polynomial not the number of terms. So here you use 2 terms, then 3 terms,. and finally 8 terms. Compare each approximation to the true value of e2.50.082084998. using the true relative...
Write a C++ program that computes the following series: sum = 1/firstPrime + 2/secondPrime+…..+1/nthPrime Your program should prompt the user to enter a number n. The program will compute and display sum based on the series defined above. firstPrime: is 2 secondPrime: the first prime number after 2 thirdPrime: the third prime number …. nth prime: the nth prime number Your program must be organized as follows: int main() { //prompt the user to enter n //read n from the...
Write VBA functions to calculate sin (x) using the Maclaurin arcsine series, and compare the values for sin-1(x) from your program to those given by the Excel spreadsheet function ASIN(x). The Maclaurin arcsine expansion is given by x 3x 6 40 (2n)! sin1(x)-2((2n+1) Note: This function by definition is only defined for-1 SxS1. When you write the code for calculating it, you will need to include code that assigns a value to it that reflects it is undefined for values...
Aer wi rié error and percent relative error. Add terms until the absolute value of the error estimate falls below an error criterion conforming to two significant figures. 3. The following infinite series can be used to approximate ex: e =1+x+ (1.3) 2 3! n! (a) Show that this Maclaurin series expansion is a special case of Taylor expansion with x 0 and h=x (b) Use Taylor series to estimate f(x)=e* at x,=1 for x = 0.20. Employ zero-, first-,...