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MTH142_Assg06

# MTH142_Assg06 - Assignment 6 Due Monday 1 Explain the...

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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
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