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Unformatted text preview: MATH 3A Final Practice Sheet Fall 2004 Instructor: G. Wei Final: Tuesday, December 7, 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 . 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 Hospitals 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 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 = s ln x + 1 ln x- 1 ; c ) .y = (cos- 1 x ) x ; d ) .y = tan(ln(cos( x 3 +1))) ....
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- Fall '07