Assignment 6 Due Monday, April 14, 2008 1. Explain the relationship between limits of functions and the concept of the derivative. (Why do we concern ourselves about limits in a calculus class? If we are taking limits of functions when we compute a derivative, what function is involved in that limit?) 2. Let f ( x ) = sin x and a = π/ 6 . In class we agreed that the limit of f ( x ) as x approaches a is L = 1 2 . That is, we agreed that lim x → π 6 sin x = 1 2 . This problem explores the meaning of this statement; throughout this problem f ( x ) = sin x and a = π/ 6 . (a) For each ± , below, compute the best δ , to four decimal places, such that if 0 < | x-a | < δ then | f ( x )-L | < ±. i. ± = 0 . 1 ii. ± = 0 . 05 iii. ± = 0 . 01 (b) Suppose ± is given and very small. What will be the ”best” choice here for δ in the limit deﬁnition? (Note that in this part of the problem, unlike part (a), you are not being given ±. Your answer should describe δ in terms of the unknown ±. ) 3. For this problem, let f ( x ) = x 3-27 x-3 and a = 3 . (a) Compute
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This note was uploaded on 04/02/2009 for the course MTH 142 taught by Professor Staff during the Spring '08 term at Sam Houston State University.