Obtain the Taylor series expansion of f(x)=e*+1 at a=0.5(the center of expansion) %3D Howlarge can the error be when (n +1) terms are used to approximate e2*+1 with x = 1?
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- Do a prediction using Taylor Expansion Series. Using a base point until finding that the error is less of a tolerence with significant figure of 1 (E8(n)>). Present the results and analize them Also for each approximation, Calculate the relative porcential iterative error iterative percentage relative error* a correction to the information above the funtion being f(x)= e^(2x) and the base values are x=1 and h=1hello calculus Use power series operations to find the taylor series at x = 0Find the power series representation of ln[1 + x] either by differentiation orintegration of the power series or by finding p(x), the Taylor series. Determinethe interval of convergence.
- I think this is Taylor series, why there is no ! mark, and what does O(x^3) mean? Continuing expansion? Nonlinear dynamic, BifurcationsA Taylor series expansion of function f (x) about some x-location x0 is given as in fig. Consider the function f (x) = exp(x) = ex. Suppose we know the value of f (x) at x = x0, i.e., we know the value of f (x0), and we want to estimate the value of this function at some x location near x0. Generate the first four terms of the Taylor series expansion for the given function (up to order (Δx)3 as in the above equation). For x0 = 0 and Δx = −0.1, use your truncated Taylor series expansion to estimate f (x0 + Δx). Compare your result with the exact value of e−0.1. How many digits of accuracy do you achieve with your truncated Taylor series?Use the power series representation 1/(1 − x)= ∞ ∑ x3, |x| < 1 N=0 to find a power series representation of f(x) = x2/(4 + x). Include the interval of convergence in your answer.
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