handout_09_28

handout_09_28 - What do you think happens at t = 3 s? 4....

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The Derivative September 28, 2009 1. Find the equation of the tangent line to the following functions at the given point. 1. f ( x ) = x 3 + 4 x at x = 1. 2. f ( x ) = 1 x + 4 at x = 0. 3. f ( x ) = x at x = 2. 2. Let f ( x ) = x 2 sin(1 /x ) for x 6 = 0 and f (0) = 0. What is f 0 (0)? 1
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3. The position of a particle at time t is x ( t ) = t 2 - 6 t +4, where x is in meters and t is in seconds. Determine the velocity of the particle at time t = 1 s and t = 4 s (give units). What does the sign signify?
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Unformatted text preview: What do you think happens at t = 3 s? 4. Each of the following limits represents the derivative of a function f ( x ) at a point a . Find such an f and such an a in each case. 1. lim h e h +3-e 3 h 2. lim x sin( x ) x 5. Sketch the graph of any function f ( x ) such that f (0) = 0, f (0) = 3, f (1) = 0 and f (2) =-1. 2...
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handout_09_28 - What do you think happens at t = 3 s? 4....

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