Consider the function f(x) = (x - 1) ln(x). (a) Find a formula for the Taylor...

 

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Consider the function f(x) = (x - 1)² ln(x). (a) Find a formula for the Taylor series of the function f(x) about the point c = 1. (b) Compute the interval of convergence of the Taylor series. (c) Suppose p4(x) denotes the Taylor polynomial of degree 4 for f(x) about the point c = 1. What is the error in approximation for p4(x) at the point x = 2? Consider the function f(x) = (x - 1)² ln(x). (a) Find a formula for the Taylor series of the function f(x) about the point c = 1. (b) Compute the interval of convergence of the Taylor series. (c) Suppose p4(x) denotes the Taylor polynomial of degree 4 for f(x) about the point c = 1. What is the error in approximation for p4(x) at the point x = 2?

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a To find the formula for the Taylor series of the function fx about the point c 1 we need to find the derivatives of fx and evaluate them at x 1 fx x ... View the full answer