sample_midterm1

sample_midterm1 - determine if they are removable: f ( x )...

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Math 016A Midterm 1 Jan., 2009 Name: ID Signature No Calculators allowed. Use the back of all the pages if needed. 1. (20pts)(a)[8pts] Given the endpoints of a diameter for a circle: (3 , 3) , ( - 3 , 3) , find the general form of the equation of the circle. (b)[12pts] Find the equations of the lines through point (2 , 1) (a) parallel, (b) perpen- dicular to the line 4 x - 2 y = 3 . 1
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2. (24pts) Compute the following limits and give each answer as a finite number, + / -∞ . (a)[6pts] lim x 3 x +1 - 1 x . (b)[6pts] lim Δ t 0 t - 1+Δ t - t - 1 Δ t . (c)[6pts] lim x →- 1 x 2 - 1 x +1 . (d)[6pts] lim x →-∞ 2 x 2 x - 1 + 3 x x - 1 · . 2
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3. (8pts) Determine the domain and range of f ( x ) = 7 - 9 - x 2 . 4. (12pts) (a) State the definition of continuity on some interval, (b) then discuss the continuity of the following function on ( -∞ , + ) . If there are discontinuities, also
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Unformatted text preview: determine if they are removable: f ( x ) = x x 2-4 x + 3 . 3 5. (14 points) Find the derivatives of the following functions: (a) f ( x ) = 3 x ( x 2-2 x ) , (b) g ( x ) = 2 x 3-4 x 2 +3 x 2 . 6. (10 points) Find the equation of the tangent line to the graph of f ( x ) = 1 3 x 2-x at point (-1 , 2) . 4 7. (12 points) The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of the Washington Monument is given by s =-16 t 2 + 555 . (a) Find the average velocity on the interval [2 , 3]. (b) Find the instantaneous velocities at t = 2 and t = 3. (c) How long will it take the dollar the hit the ground? (d) Find the velocity of the dollar when it hits he ground. 5...
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This note was uploaded on 12/04/2009 for the course MATH 69453 taught by Professor Duanekouba during the Spring '08 term at UC Davis.

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sample_midterm1 - determine if they are removable: f ( x )...

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