MATH 180 Study Guide - Final Guide: Asymptote
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Solution: the limit is indeterminate because, upon substituting = 0, the function value tends toward 0/0. This indeterminacy may be resolved by rewriting tan as sin / cos to yield lim. 0 tan tan tan tan tan sin / cos sin . If we let x = 2 , then the limit becomes lim. Problem 2 solution: use the squeeze theorem to nd lim x 0 x2 cos(cid:18) 1 x3(cid:19). Solution: using the fact that 1 cos 1 for all we have the following inequalities: X2 x2 cos(cid:18) 1 x3(cid:19) 1 x3(cid:19) x2 for all x 6= 0. Since lim x 0 ( x2) = lim x 0 x2 = 0 we have, by the squeeze theorem, lim x 0 x2 cos(cid:18) 1 x3(cid:19) = 0. Problem 3 solution: find all horizontal and vertical asymptotes of f (x) = calculus. x2 + 3x 4 x2 2x + 1.
