APPM 1350 Midterm: appm1350fall2016exam1_sol

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31 Jan 2019
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Explain how each x-value fails to satisfy the de nition of continuity. Be speci c and provide details in your answer. Solution: (a) (2 pts) 2 (b) (2 pts) 5 (c) (3 pts) f (a) = lim x a f (x) Also acceptable: f (a) = lim x a or. 3-part de nition: f (a) exists, lim x a f (x) = lim x a+ f (x) f (x) exists, and f (a) = lim x a f (x). (d) (9 pts) f is discontinuous at x = 4, 1, 6 . At x = 4, f ( 4) does not exist. At x = 1, lim x 1 is 2. 2x csc(5x). (b) find lim t 1 (c) consider lim h 0. Justify your answer: find the instantaneous rate of change of g at x = 4 /3. = lim t 1+ t + 1 (t + 1)(t 1)

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