MATH 180 Study Guide - Final Guide: Quotient Rule, Even And Odd Functions, Indeterminate Form
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Problem 1 solution: compute each limit or explain why it does not exist. (a) lim x 3 (b) lim x . 1 x2 1 sin(x) x (c) lim x 2. 3x + 10 4 x 2. Solution: (a) the function f (x) = limit via substitution. 1 x2 1 is continuous at x = 3. 8 (b) the limit must be evaluated using the squeeze theorem. 1 x for all x > 0. Furthermore, we know that sin(x) x x (cid:18) lim. Therefore, by the squeeze theorem, we have lim x sin(x) x. = 0. (c) upon substituting x = 2 we nd that the limit is of the form 0. We have two options: (1) use an algebraic method or (2) use l"hopital"s rule. 1 use an algebraic method, i. e. multiply by the conjugate divided by itself. 3x + 10 + 4 x 2 (3x + 10) 16.
