PROVIDE PYTHON CODE: Use zero-through forth order Taylor series expansion to predict f(2.5) for f(x) = lnx using a base pint at x = 1. Compute the true percent relative error for each approximation using python and explain your results in detail.
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PROVIDE PYTHON CODE:
Use zero-through forth order Taylor series expansion to predict f(2.5) for f(x) = lnx using
a base pint at x = 1. Compute the true percent relative error for each approximation using python and
explain your results in detail.
Step by step
Solved in 4 steps with 2 images
- Realize the following approximation of the sin(x) function.. sin x ~ 00 L i=0 (-1)⁰ (2i + 1)! -x2i+1 = x x3 x5 x7 + 3! 5! 7! The approximation is based on the Maclaurin series expansion, and it becomes an equality (i.e. not only an approximation) as the summation continues to infinity. Your program will check if the approximation error falls below 1e-15, and stops if so. Otherwise, it will continue to a maximum of 100 summations. Your program should ask the user about the angle (in radians) which they want to find the sin() of. Notice that the user will only input an angle in radians and in the range [0-pi]. Use a while loop to answer the question. Use the following definition for the approximation error: Error = abs(true value - approximation) / true value Hint: you need two loops, where one goes through the summation, and the other is dedicated to calculating the factorials. Hint: The angle must be expressed in radians and must be in the range [0-pi]. Use such numbers when testing…Derive the formula to get the third forward finite difference (x+3h) to get the coefficient of forward finite difference approximation O(h^3) Notes: Get the coefficients on the third line only Reference: Numerical Methods in Engineering with python 3” Jaan Kiusalaas pp. 183-187Please provide me with python code do not solve it on paper verify mean value theorem for the following functions on the following intervals f(x) = a2 +2x – 1, (0, 1).
- Use MATLAB to: (a) Approximate the roots of the function f (x) defined by: f(x) = x² sin(x) (b) Calculate the roots of f (x) as defined in part (a) in a span of [-6, 6]. (c) Estimate a function g(x) by deriving the Taylor series of the function (x) up to order 8. (d) Calculate the roots of the Taylor series in the span of [-6, 6].Write a computer program to evaluate the Taylor series expansion for cos(x) to evaluate theseries starting at x0 = 0 radian with h = 0·1 to x = 1 radian· Use one term, two terms, three termsand four terms of the series· Evaluate the error in each value and discuss the effect ofincrementally adding the terms to the series· Compare your results with the true solutionUsing MatLab to code the exponential equation symbolically, use the built in integral function, int( ) to find the kilo-Watt-hours produced in a day: f(t) = e(-t-12)/(1.5*root(2pi)
- Problem 3 Determine the root/s of the following graphically: (Using Matlab/Python) a. f(x) = x³ + 3x² 9 b. first positive root of f(x) = sin (x) + cos (1 + x²) – 1 where x is in radian. c. f(x) = e-0.5x (4 - x) — 2calculate sin (0.3π) to 8 significant figures using the maclaurin series expansion of sin(x). Need a solution in C or Mathematica as a codeUsing MATLAB functions poly and polyder, compute the relative condition numbers of the roots 1, 2, ..., 20 of the Wilkinson polynomial 20 w(x) = (x1)(x-2)(x - 20) = x²0 210x¹⁹+... 19 with respect to perturbation of the coefficient of 2x¹⁹, a19, from -210 to -210+2-23 Present your results in a tabular form and write your conclusion on the ill-conditioninig of the Wilkinson polynomial. (Recall: condition number for the jth root is kj |a₁x²=1| \w'(x₂)
- Using MATLAB, develop a computer program for the finite difference solution with general θ scheme for the 1D consolidation of a uniform layer of soil. Compare the results for θ=0, 0.5, 2/3 and 1.0 for α=0.49 and α=0.51 against the analytical solution of Terzaghi’s equation for T=0.5. Apply the program to both cases of double draining layer and single draining layer.Q. Taylor Series expansion of sine for x is computed as follows: sin x=x - x^3/3! + x^5/5! - x^7/7!+... Let the value of x be 30, hence radian value for 30 degree is 0.52359 sin(0.52359) = 0.52359 - 0.52359^3/3! + 0.52359^5/5! - 0.52359^7/7!+ ... (a)Write a function in c++ that takes value of x in degrees and returns the value of x in radians. (b)Write a function in c++ that calculates and returns the factorial of a number.e.g. 3!=6 (c)Write a function in c++ that calculates and returns power of a number. e.g. 23=8. (d)Use the above three functions to find the taylor expansion of sine for in degrees as given above.(Calculate first 3 terms)Please use python code Use Gauss-Laguerre quadrature to evaluate integral from 0 to infiniti(1-x^2)^3e^-xdx.