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FinalMC2005

# Calculus: Early Transcendental Functions

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1. If y 2 3 x y = 18, then dy ccccccc dx at the point H 1, 3 L is H A L 1 H B L 0 H C L 1 H D L 4 cccc 3 H E L 8 cccc 3 2. The equation of the line tangent to the curve y = k x + 8 cccccccccccccccc k + x at x = − 2 is y = x + 4. The value of k is H A L 3 H B L 1 H C L 1 H D L 3 H E L 4 3. If f H x L = 3 x 2 and f H 2 L = 1, then find 0 2 f H x L dx H A L 2 H B L 4 H C L 9 H D L 16 H E L 22 4. The figure below shows the graph of the acceleration of an object moving on the x axis as a function of time. Assume that v H 0 L = 0. Among the 5 marked points, which time corresponds to the greatest speed of the object? t a H t L A B C D E a H t L H A L A H B L B H C L C H D L D H E L E 5. Find lim x 1 4 ccc x 4 ccccccccccccccc x 1 H A L 4 H B L 1 H C L 1 H D L 4 H E L Does not exist 6. If y = f H x 3 L and f H x L = è!!!!!!!!!!!!!!! 3 x 2 then dy ccccccc dx is equal to H A L è!!!!!!!!!!!!!!!!! 9 x 2 2 H B L x 3 è!!!!!!!!!!!!!!!!! 3 x 3 2 H C L 3 x 2 è!!!!!!!!!!!!!!!!! 9 x 2 2 H D L 3 x 2 è!!!!!!!!!!!!!!!!! 3 x 3 2 H E L 18 x 3 è!!!!!!!!!!!!!!!!! 9 x 2 2 7. Determine which of the following is not true for f H x L = a x , a > 1 H A L f H 0 L = 1 H B L f H 1 L = 0 H C L lim x → −∞ f H x L = 0 H D L lim x → ∞ f H x L = ∞ H E L lim x → ∞ f H x L = ∞ 8. If f H x L = x 3 + 8, and g H x L is the inverse function of f, then g H 0 L is equal to H A L 1 ccccccc 12 H B L 1 ccccccc 3 H C L 1 cccc 3 H D L 1 ccccccc 12 H E L Not enough information to determine g H 0 L

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9. Suppose that f and g are continuous functions, and that 1 3 f H x L dx = 10, 1 3 g H x L dx = 2, 1 3 f H x L dx = 1, and 1 3 g H x L dx = 8, then find 1 1 H 2 f H x L g H x LL dx H A L 12 H B L 18 H C L 24 H D L 36 H E L Not enough information is given 10. Suppose f H x L = è!!!!!!!!!!!!
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FinalMC2005 - 1 If y2 3 x y = 18 HA L 1 2 then HBL 0 dy at...

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