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Category: Limit

Computing Limit As A Derivative

July 2nd, 2009, 1 Comment

Recall that if a function is differentiable at then . Now if the derivative of is easy to compute, then we can use it to compute the limit of the same form as the above. Here are three examples ( Review Problems on Stewart’s Calculus, Chapter 3, problem 106,107 and 108) Problems Compute the following [...]

Factorization In Disguise (2.3.61)

June 24th, 2009, 2 Comments

Stewart Calculus 2.3.61 Find such that the limit exists. Solution Suppose the limit exists and equal to . Note that for . Then by the limit laws we have . On the other hand . Thus and therefore . Now we will show that if then the limit exists. For we have

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