2011a_x2b_sols

2011a_x2b_sols - Spring 2011 Math 151 Exam II Version B...

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Unformatted text preview: Spring 2011 Math 151 Exam II Version B Solutions 1. E Differentiate to find the velocity: s ( t ) = 6 t 2 42 t + 72 , so s (1) = 36 . 2. D If you dont just remember the key limit, multiply by the con- jugate: lim x 1 cos x 2 x 1 + cos x 1 + cos x = lim x 1 cos 2 x 2 x (1 + cos x ) = lim x sin 2 x 2 x (1 + cos x ) = lim x sin x x sin x 2(1 + cos x ) = 1 0 = . 3. A g (2) = 1 f ( g (2)) . f ( x ) = 3 x 2 + 1 . To find g (2) , let y = g (2) . Then 2 = f ( y ) = y 3 + y . By inspection, y 3 + y = 2 when y = 1 . So g (2) = 1 f (1) = 1 4 . 4. B Switch x and y and solve for y : x = y 5 , so x 2 = y 5 and y = x 2 + 5 . The domain of f 1 is the range of f , which is [ , ) . 5. D dy dx = dy/dt dx/dt = 3 t 2 2 t 4 . When t = 2 , dy dt = 12 and dx dt = 0 , so the graph has a vertical tangent at t = 2 . When t = 2 , x = 2 2 4(2) + 1 = 3 , so the equation is x = 3 ....
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This note was uploaded on 02/13/2012 for the course MATH 151 taught by Professor Artbelmonte during the Spring '06 term at Texas A&M.

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2011a_x2b_sols - Spring 2011 Math 151 Exam II Version B...

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