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Unformatted text preview: 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 → + (sin x ) ln x (c) lim x → 1 (ln x ) ln x (d) lim x → ln2 sinh x- 3 4 x- ln 2 (e) lim x →∞ x- √ x 2 + x (f) lim x → sin 1 x (g) lim x → x sin 1 x 6....
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This note was uploaded on 02/15/2010 for the course IPHY 4540 at Colorado.