Unformatted text preview: (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. 4. Given the function f ( x ) = (1 + 2 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 . 5. Given the function y = √ x 2 + 5 (a) [9 pts. ] Use the limit deﬁnition of the derivative to ﬁnd dy dx . (b) [9 pts. ] Use the Power Rule combined with the Chain Rule to ﬁnd the derivative with respect to x . 6. [8 pts. ] Given that h (2) = 3 and h (2) = 4, evaluate the derivative of f ( x ) = h ( x ) + 5 x + 2 with respect to x when x = 2. 7. [8 pts. ] Find the derivative of xcos ( y ) = sin (2 x + 2 y ) with respect to x . Bonus : [2 pts. ] Simplify cos ( arcsin ( 1 5 ))....
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 Spring '10
 AmandaSmith
 Math, Calculus, Derivative, pts, blue book, North Carolina State, limit deﬁnition

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