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04_Midterm1-Sample

# 04_Midterm1-Sample - f x has a zero in the interval[0...

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University of California, Riverside Department of Mathematics Midterm 1 Mathematics 9A - First Year of Calculus Sample 4 Instructions: This exam has a total of 33 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. Evaluate the following limits. (sections 2.2, 2.4 and 2.5) (a) (3 points) lim x ! 2 p x 2 +12 ° 4 x ° 2 (b) (3 points) lim x ! 0 sin(3 x ) sin(7 x ) (c) (3 points) ( lim x ! ( ° 2 ) ° tan x 2. The function f ( x ) = 3 x 7 ° 8 x + 2 is a polynomial and therefore con- tinuous everywhere. (a) (3 points) State the Intermediate Value Theorem. (b) (3 points) Use the Intermediate Value Theorem to show that

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Unformatted text preview: f ( x ) has a zero in the interval [0 ; 1] : (section 2.6) 3. (6 points) Use the de&nition of the derivative to &nd dy dx for the function y = 1+ x 3 x . (section 3.1) 4. Find the derivatives of the following functions. Do not simplify. (sections 3.2, 3.4 and 3.5) (a) (3 points) f ( x ) = x 3 sin ( x 4 ) (b) (3 points) f ( x ) = x 3 tan ( 3 x 3 ) (1 & 6 x ) 1 5. (6 points) A spaceship that is stationery in outer space &res a projec-tile which travels horizontally in a straight line. Its position from the spaceship is given by the function: s = t 2 + 4 t where s is in meters and t is in seconds. What is the velocity of the projectile when it is 12 meters from the spaceship? (section 3.3) 2...
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04_Midterm1-Sample - f x has a zero in the interval[0...

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