MATH116 Lecture Notes - Lecture 17: Flac, Product Rule, Logarithmic Differentiation

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004 (che) (cive: dunbar, girelli (geoe/enve) e. dupont (me, beltaos. Instructions: write your name, email, id and section number at the top of this page, answer the questions in the spaces provided. There are questions on both sides of the page. There is a blank page at the end of the exam for rough work: show all work required to obtain your answers for full credit. 1. (a) di erentiate r(x) = x20 + 14. [3] (b) di erentiate g(x) = tan 1(x2): (continued) (c) di erentiate h(x) =(cid:82) x. [3] (d) calculate the limit lim x 0+ xtan(x). [3: (a) use logarithmic di erentiation to prove the product rule (f (x)g(x)) = f(cid:48)(x)g(x) + f (x)g(cid:48)(x). d dx. You may assume that f and g are positive: (continued) If not, prove that no such function exists. Iterative procedure on the function f (x) = x2 10 with an initial guess of x1 = 3.

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