Test2B - s ( t ) = 160 t-16 t 2 feet after t seconds. (a)...

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MA141-001 Test 2 B February 24, 2010 Amanda Smith North Carolina State University Department of Mathematics Please put all work in the stamped blue book that has been provided. Nothing on this test sheet will be graded. Please put one problem on each page; you are allowed to use the back of the sheet as a new page. No calculators, formula sheets, or other aids are permitted. Please show all of your work. Simplify all solutions completely and clearly indicate your answers. Write your name on both the blue book and this test sheet. 1. Given the function f ( x ) = (2 + 3 x ) 2 + x 3 (a) [9 pts. ] Find the first derivative of f ( x ) with respect to x . (b) [9 pts. ] Find the second derivative of f ( x ) with respect to x . 2. [8 pts. ] Using the limit definition of the derivative, find an equation of the tangent line to the hyperbola y = 3 x at the point on the hyperbola (3 , 1). 3. [8 pts. ] Find the derivative of xcos ( y ) = sin (3 x + 3 y ) with respect to x . 4. A toy rocket fired straight up into the air has height
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Unformatted text preview: s ( t ) = 160 t-16 t 2 feet after t seconds. (a) [8 pts. ] Find the time when the rocket smashes into the ground. (b) [8 pts. ] Find the velocity of the rocket at time t. (c) [8 pts. ] Find the velocity of the rocket 2 seconds after the launch. (d) [8 pts. ] Find the acceleration of the rocket at time t. 5. [8 pts. ] Dierentiate y = ( x 3 + 3 x + 6) 5 ( x 2 + 2) 4 with respect to x . 6. Given the function y = x 2 + 3 (a) [9 pts. ] Use the limit denition of the derivative to nd dy dx . (b) [9 pts. ] Use the Power Rule combined with the Chain Rule to nd the derivative with respect to x . 7. [8 pts. ] Given that h (2) = 2 and h (2) = 3, evaluate the derivative of f ( x ) = h ( x ) + 4 x + 2 with respect to x when x = 2. Bonus : [2 pts. ] Simplify cos ( arcsin ( 1 3 ))....
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