please #3, 5, 7, 13, 17, 19, 23, 37

A 1. (a) Find the Taylor polynomials up to degree 5 for 23. Use the information from Exercise 5 to estimate cos 80 f(x) = sin x centered at a = 0. Graph f and these correct to five decimal places. polynomials on a common screen. (b) Evaluate f and these polynomials at x = TT/4, TT/2, 24. Use the information from Exercise 16 to estimate sin 38 and TT. correct to five decimal places. (c) Comment on how the Taylor polynomials converge 25. Use Taylor's Inequality to determine the number of terms of to f(x). the Maclaurin series for e* that should be used to estimate 2. (a) Find the Taylor polynomials up to degree 3 for el to within 0.00001. f(x) = tan x centered at a = 0. Graph f and these 26. How many terms of the Maclaurin series for In(1 + x) do polynomials on a common screen. you need to use to estimate In 1.4 to within 0.001? (b) Evaluate f and these polynomials at x = T/6, TT/4, 27-29 Use the Alternating Series Estimation Theorem or and TT /3. Taylor's Inequality to estimate the range of values of x for which (c) Comment on how the Taylor polynomials converge the given approximation is accurate to within the stated error. to f(x). Check your answer graphically. 3-10 Find the Taylor polynomial 73(x) for the function f centered at the number a. Graph f and 73 on the same screen. 27. sin x ~ x - 6 (| error |