Problem 1: a) (1.5 marks )Find the approximation T10 (using the Trapezoidal rule) for 1 / exdw. 0 Find the actual error produced in using this method of approximation. b) (1.5 marks) Find the upper bound on the error term [ETI and compare this to the actual error you found in part a). c) (2 marks) How large do we need to choose 72 to guarantee the estimate of Tn for the integral in part a) is accurate to 0.00001? Round all answers in parts a), b) and c) to 8 decimal places. .0 EV |MG_9530.heic Problem 2: (5 marks) Is the series i(_1)nl ln(\") 7?. absolutely convergent, conditionally convergent, or divergent? Make sure to Show all your work and indicate clearly all tests that are used to determine the correct answer. Problem 3: Let f(x) = 1+2 + 22 + 23 + 24 + 25. 1. (1 mark) Find 73(x), the Taylor polynomial of f at x = 0 with degree 3 by using the definition of Taylor polynomials. Note that no partial mark will be given if the answer does not show work of using the definition of Taylor polynomials. 2. (1 mark) Find the remainder Rs(x) = f(x) - T3(x). 3. (1 mark) Find the maximum value of f (4) (x) on the interval x |