MATH 201 Exam 2, Fall 2013

Math 201 Practice Problems for Quiz I 1) Find the following limits. Justify your answer. 2) Investigate convergence/divergence of the following series Warning: The big hints/tricks below will not be given on the Quiz (but very easy to remember!) f) (Warning: “getting closer to 1” fails) 3) Find the domain of convergence of the following power series. Also indicate absolutely or conditionally. a) 4) a) Find according to the values of c the series sum Telescopic) b ) What can you say about (Hint: One of the cases of convergent /divergent is easily seen to be impossible!) 5) Find (Hint : Use if this last exists) Careful !!! 5*| Find (Hint : Use if this last exists) 6a) p. 583: 39, 40, 42 ( MORE “Find interval of convergence”) 6b) p. 608: 20, 27 (MORE LCT problems) 7) Let . Find (via the Maclaurin series of f(x). 8) Let (i) Find the Taylor series of f(x) at a=2 with its domain of convergence. (Hint: x=2+(x-2)) (ii) Find 9) Find value of the following 10) 10.10 (p. 603) : 15, 17, 20,22 Estimate the definite integrals (in such problems) by using the first two non-zero terms of the relevant series 10*) 10.10 (p. 603) : 25, 59, 55, 5 11) Suppose . Moreover, (a) Find the Maclaurin series of f (x). (b) Show that = its Maclaurin series (c) Find the exact value of (Look carefully at its series) (d) If we approximate f(x) ~ P10 (where P10 is the Maclaurin polynomial of f (x)), estimate the error in such approximation on the interval 0 < x < 2. 12) (Discovery) Find (Yes: ln n is increasing) & deduce