1. (A) Use the Taylor series expansion for the sin x to estimate sin(t/4) for the...
Important: Please make sure assignment should be stapled if it is more than one sheet. The following deductions will be applied: you print the assignment sheet and write you solution on it. The submitted Submitting your assignment on a sheet other than given template: 2. Submitting your assignment loose and not stapling it. 1. %15 deduction %15 deduction 1. Use the Maclaurin (Taylor) series expansion for the sin x to estimate sin(/4) for the acceptable relative errors of 0.25 and...
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...
Can someone walk me through how to do question 2 with all the proper work shown? Horne, vork # 3 MİATH 1206 Show all work! 1. (10 pts) Find the Taylor series expansions for f(x) = sin at z = 0 and x = 3, Find the radius of convergence for these series. 2. (5 pts) Find the Taylor series expansion for f(x) = 1/z at 2. 3. (5 pts) Find the sum of the serics rA 5nn! 4" (5...
Setup a program that will solve for sin x using the Taylor series expansion of x. Make sure the number of terms is some type of input. Calculate approximate 1. error Setup a program that will solve for sin x using the Taylor series expansion of x. Make sure the number of terms is some type of input. Calculate approximate 1. error
An alternative way for calculating sin(x) is to use its Taylor series as the following: sinx)x-+ Create a function named "sin_taylor" in MATLAB. This function takes two inputs. First input is the angle, and the second input determines the number of terms in Taylor series for approximation. Check the fidelity of your function by running sin-taylor( 7) and compare it with the exact value of it. Hint: “factorial" is a built-in function that you can use for calculating factorial of...
2. Use the definition of Taylor series to find the Taylor series of f(x)=sin(2x), centered at ca. You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. 4
need answer for #2, which is about arctan #1 Suppose we want to estimate sin (0.1) using the Taylor series of sin x at x = 0. (a) Find roughly a number of nonzero terms which are required to compute sin(0.1) to n decimals (you do not need to find the minimum number.) (b) Find such a number more accurately, i.e. find a smaller one, using any mathematical tech niques. You may want to use the fact related to Stirling's...
solve 2-3 1. Use a Taylor series to get the limit: In(x+3) 2. Use a Taylor series to get the derivative of f(x) = arctan x and check for the interval of convergence. Is the interval of convergence for f' the same as the interval for for different? Why? 3. Use a Taylor series to solve y' (t) - 3y = 10,y(0) = 2
3. A nonlinear system: In class we learned how to use Taylor expansion up to the 1* order term to solve a system of two non-linear equations; u(x.y)- 0 and v(x.y)-0. This method is also called Newton-Raphson method. (a) As we did in lecture, expand u and v in Taylor series up to the 1st order and obtain the iterative formulas of the method. (In the exam you should have this ready in your formula sheet). 1.2) as an initial...
Please use matlab to solve the question. 1. The following infinite series can be used to approximate e*: 2 3! n! Prove that this Maclaurin series expansion is a special case of the Taylor series (Eq. 4.13) with Xi = 0 and h a) x. b) Use the Taylor series to estimate f(x) e* at xH1 1 for x-0.25. Employ the zero-, first-, second- and third-order versions and compute the letlfor each case. Take the true value of e10.367879 for...