Assignment 6Due Monday, April 14, 20081. Explain the relationship between limits of functions and the concept of the derivative. (Why do weconcern ourselves about limits in a calculus class? If we are taking limits offunctionswhen wecompute a derivative, what function is involved in that limit?)2. Letf(x) = sinxanda=π/6.In class we agreed that the limit off(x) asxapproachesaisL=12.That is, we agreed thatlimx→π6sinx=12.This problem explores the meaning of this statement; throughout this problemf(x) = sinxanda=π/6.(a) For each, below, compute the bestδ, to four decimal places, such that if 0<|x-a|<δthen|f(x)-L|<.i.= 0.1ii.= 0.05iii.= 0.01(b) Supposeis given andverysmall.What will be the ”best” choice here forδin the limitdefinition? (Note that in this part of the problem, unlike part (a), you are not being given.Your answer should describeδin terms of the unknown.)3. For this problem, letf(x) =x3-27x-3and
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