APPM 1350 Midterm: archive_appm1350summer2018exam1_sol
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Summer 2018: let f (x) = 2 + Justify your answer using limits. (c) [9 pts] find the asymptotes of f . 2 2x (x 1)(x 4) The denominator vanishes if x = 1 or x = 4. = lim lim x 4 f (x) = lim x 4(cid:18)2 + x 4(cid:18)2 + 2. = x = 1 is a removable discontinuity x 1(cid:18)2 + x2 5x + 4(cid:19) = lim. 2 2x x 4(cid:19) = 2 + 2. 2 2x x 4(cid:19) does not exist = x = 4 is not a removable discontinuity (x 1)(x 4)(cid:19) 2(1 x) (c) candidates for vertical asymptotes are points where f (x) is not de ned, namely x = 1 and x = 4. We have already shown that x = 1 is a removable discontinuity. Checking x = 4, lim x 4+ f (x) = lim x 4+(cid:18)2 + x 4+(cid:18)2 + 2 x2 5x + 4(cid:19) = lim.
