Problem 3: Consider the following function. f(x) = 0.5x + cosx a) Use Taylor Series to...

 

 

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Problem 3: Consider the following function. f(x) = 0.5x + cosx a) Use Taylor Series to approximate the function if the initial point is 0.5. Estimate the function at x = 2 using a third-order Taylor Series. Estimate the truncation error. b) Use the Central, Backward, and Central Difference Methods to approximate the 1st derivative. Which method is the most accurate. Use h = 0.2 and x0 = 0.6 Problem 3: Consider the following function. f(x) = 0.5x + cosx a) Use Taylor Series to approximate the function if the initial point is 0.5. Estimate the function at x = 2 using a third-order Taylor Series. Estimate the truncation error. b) Use the Central, Backward, and Central Difference Methods to approximate the 1st derivative. Which method is the most accurate. Use h = 0.2 and x0 = 0.6