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# 05fp - MATH 3A Final Practice Sheet Spring 2005 Instructor...

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MATH 3A Final Practice Sheet Spring 2005 Instructor: G. Wei Final: Monday, June 6, Buchn 1940, 7:30-10:30pm 1. A particle moves along a straight line whose position is recorded by the function s = t 3 - 6 t 2 + 3 t + 1 , t 0 . a). Find both the velocity and acceleration of the particle at time t . b). When is the particle moving forward and when is it moving backward? c). Find the acceleration when the velocity is zero. 2. Find the tangent line of the curve x 3 y + 2 xy 3 = 3 at the point (1 , 1). 3. Compute the following limits (you are not allowed to use L ´ Hospital’s rule for the first one; the rest you can use any method): lim x 5 3 x + 1 - 4 x - 5 . lim x →-∞ 4 x 2 + 3 x + 1 x + 2 . lim x 0 csc x - cot x x . lim x →∞ ln ln x x . 4. Find the derivatives of the following functions a ) .y = tan(3 x 2 ) sin x ; b ) .y = ln x + 1 ln x - 1 ; c ) .y = (cos - 1 x ) x ; d ) .y = tan(ln(cos( x 3 +1))) . 5. Find the derivative of f ( x ) = x x +1 using only the definition of derivative as a limit. (You will not get any credit for using the differentiation rules.) 6. Find all critical points of

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05fp - MATH 3A Final Practice Sheet Spring 2005 Instructor...

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