APPM 1340 Midterm: archive_appm1340fall2018exam2
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Instructions: outside paper and electronic devices are not permitted. Unless indicated, answers with no supporting work may receive no credit. Box your nal answers: (24 points) consider the functions g(x) = 2 2x and h(x) = x2 5x + 4 (a) consider f (x) = 2 + g(x) h(x) Find any discontinuities and label them as asymptotes or holes. List the (x, y) coordinates of any hole. Use the de nition of vertical asymptote to show any asymptotic behavior. (b) consider k(x) = h(x) + 5x 4 q 1. Use the ivt to show that there is a real number such that k(x) = 4. (c) find lim x . [(g/h)(x): (10 points) show that the function f (x) = (cid:26) |x3 + 1| 2 x2 x 3 x < 1 x = 1. Turn over exam, more on the back: (12 points) no work is required for the following questions.
