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FinalMC2006

# Calculus: Early Transcendental Functions

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Unformatted text preview: 1. â€¡ x cccccccccccccccc ccccc Ã¨!!!!!!!!!!!!!! x 2 + 4 3 dx = H A L 1 cccc 6 ln H x 2 + 4 L + C H B L 3 cccc 4 H x 2 + 4 L 2 ccc 3 + C H C L 3 cccc 8 H x 2 + 4 L 4 ccc 3 + C H D L 1 cccc 3 H x 2 + 4 L 2 ccc 3 + C H E L 2 cccc 3 H x 2 + 4 L 4 ccc 3 + C 2. A particle moves on the x âˆ’ axis. The velocity of the particle is shown in the graph below. At what value H s L of t does the particle change direction? 1 2 3 4 5 6 7 t âˆ’ 2 âˆ’ 1 1 2 3 y v H t L H A L t = 2 and t = 5 H B L t = 4 and t = 6 H C L t = H D L t = 7 H E L nowhere 3. If f H x L = x 3 âˆ’ x 2 + 3 x âˆ’ 1 and f H 1 L = 2, find g Â¡ H 2 L if g H x L = f âˆ’ 1 H x L H A L âˆ’ 2 H B L âˆ’ 1 cccc 4 H C L 1 cccc 4 H D L 1 cccc 2 H E L 2 4. An equation of the line tangent to the graph of y = 3 x + 1 cccccccccccccccc ccccc 4 x âˆ’ 3 at the point H 1, 4 L is H A L âˆ’ 13 x + y = âˆ’ 9 H B L x âˆ’ 13 y = âˆ’ 51 H C L x + 13 y = 53 H D L 13 x + y = 17 H E L 3 x âˆ’ 4 y = âˆ’ 13 5. If y 2 âˆ’ x 2 = 2 x, find d 2 y ccccccccc dx 2 at the point I 1, Ã¨!!! 3 M H A L âˆ’ 3 Ã¨!!! 3 H B L âˆ’ 1 cccccccccccc 3 Ã¨!!! 3 H C L 1 ccccccccccccc 3 Ã¨!!! 3 H D L Ã¨!!! 3 H E L 3 Ã¨!!! 3 6. If f H x L = 2 x + 1 cccccccccccccccc ccccc x + 3 , then the inverse function, f âˆ’ 1 , is given by f âˆ’ 1 H x L = H A L 3 x âˆ’ 2 cccccccccccccccc ccccc 1 âˆ’ x H B L x âˆ’ 3 ccccccccccccccc 2 âˆ’ x H C L 3 x âˆ’ 1 cccccccccccccccc ccccc 2 âˆ’ x H D L 2 x âˆ’ 3 cccccccccccccccc ccccc 1 âˆ’ x H E L x âˆ’ 2 cccccccccccccc 3 âˆ’ x 7....
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