2. Use zero- through third-order Taylor series expansions to predict f (3) for f(x) = 25 x3 - 6x2 + 7x- 88 using a base point at x = 1. Compute the true percent relative error & for each approximation.
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- Find the Taylor series for f(x) = 6/(1 − 2x)^21. Use zero-through third-order Taylor series expansions to predict (3) for fix)=25x³-6x² + 7x+88 using a base point at x = 1. Compute the true percent relative error &, for each approximation. h = 3-1=2 Record your result on the table. 2.. Use zero-through third-order Taylor series expansions to estimate f(x) = e-* using a base point at x = 1 for x = 0.2. Compute the true percent relative error E, for each approximation. A = 0.8 Record your result on the table. Order 0 1 2 3 Order 0 1 2 3 Value Value E₁ E₁Q4: drive the Taylor series for (x + 2)e* for x = -2
- 4. Find a power series representation for f(x) = 9 + x2Find the Taylor Series for the function f(x) = ax3 + bx2 + cx + d about the point x = 2. What is the coefficient of the linear term (x- 2) if a = 13.1, b = 9.4, c = 9.3, and d = 21.9. *Please answer with complete solution. Don't round off. Thanks.2. Use the Binomial Theorem for the expansion of the function as a power series. f(x) = V1+ 3x²
- find the taylor series for f(x)= 1/1-4x at x=24. Find a power series representation for the function f(x) = RY and determine the radius of conver- gence.Estimate the following function with the Taylor series at xi+1 = 0.5 for xi = 0.1. Use the zeroth, first, second, third, fourth and fifth order versions andEstimate the actual error value (%) for the version (take three decimal places)? f(x) = x5 - x4 - 5x3 - x2 + 4x + 3