Consider the function f(x) = ln(1 + x) a) Obtain Taylor series of f(x) around x...

  

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Consider the function f(x) = ln(1 + x) a) Obtain Taylor series of f(x) around x = 0. Write down the procedure in detail, not just the final outcome. b) Write a MATLAB user-defined function that evaluates f(1), using Taylor series, for a given number of terms. For this purpose, first write a pseudo-code or step- by-step algorithm and include it in your submission. c) Test your program for increasing numbers of terms in the series. Create a plot that shows how many significant digits of precision you obtain in your answer as a function of the number of terms in the series. How many terms are necessary to reach machine precision (that is, order of ~ 10-¹6)? Consider the function f(x) = ln(1 + x) a) Obtain Taylor series of f(x) around x = 0. Write down the procedure in detail, not just the final outcome. b) Write a MATLAB user-defined function that evaluates f(1), using Taylor series, for a given number of terms. For this purpose, first write a pseudo-code or step- by-step algorithm and include it in your submission. c) Test your program for increasing numbers of terms in the series. Create a plot that shows how many significant digits of precision you obtain in your answer as a function of the number of terms in the series. How many terms are necessary to reach machine precision (that is, order of ~ 10-¹6)?

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a To obtain the Taylor series of fx ln1x around x 0 we need to find the derivatives of fx and evaluate them at x 0 to determine the coefficients of the Taylor series 1 First derivative fx 11x Evaluate ... View the full answer