02_Midterm2-Sample

02_Midterm2-Sample - University of California Riverside...

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University of California, Riverside Department of Mathematics Midterm 2 Mathematics 9A - First Year of Calculus Sample 2 Instructions: This exam has a total of 100 points. You have 50 minutes. You must show all your work to receive full credit You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Compute the derivative of each of the following functions. You do not need to simplify your answers. (a) (6 points) f ( x ) = (2 x 3 + 3 x ) 4 ( x 5 3 x 3 + 7) 2 = 3 (b) (6 points) g ( x ) = sin x 1+4 x + x 3 (c) (8 points) h ( x ) = cos sec 1 ( x 2 +1) 3 ±± 2 y 2 + 3 xy 2 x 2 = 40 (a) (10 points) Using implicit di/erentiation, compute dy dx . (b) (10 points) Find the coordinates of each point on the curve which has a horizontal tangent line. 3. A weight is allowed to move upwards and downwards while suspended
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02_Midterm2-Sample - University of California Riverside...

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