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finalreviewpacket_pn - Calculus I Final Review 1 Find an...

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Calculus I Final Review 1. Find an equation for an exponential function through the points (1 , 5), (3 , 12) and with hori- zontal asymptote y = 0. Find another equation when the asymptote is y = 20 . 2. Suppose the half-life of a radioactive isotope is 125 days. How many days will it take for a sample of the substance to reach 10% os its starting amount. 3. A sinusoid has a minimum at (32 , - 2) and a maximum at (38 , 8) with no critical points in between. Find two equations for this function, one in terms of sin and the other in terms of cos . 4. Let f ( x ) = x 3 - 2 x 2 + 3 x - 2 if x c 2 x - 2 if x > c for some constant c. For what value(s) of c is f continuous? Differentiable? 5. Evaluate the following: (a) lim x →∞ ln x 8 x 2 + 1 (b) lim x 0 + (sin x ) ln x (c) lim x 1 (ln x ) ln x (d) lim x ln 2 sinh x - 3 4 x - ln 2 (e) lim x →∞ x - x 2 + x (f) lim x 0 sin 1 x (g) lim x 0 x sin 1 x 6. t (sec) 0 1 2 3 4 5 v ( t ) (ft/sec) 40 32 26 22 20 19 (a) Approximate the instantaneous acceleration t = 2 sec.
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