03_Midterm1-Sample

03_Midterm1-Sample - j f ( x ) & L j...

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University of California, Riverside Department of Mathematics Midterm 1 Mathematics 9A - First Year of Calculus Sample 3 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 ::: . exist, provide a reason why the limit does not exist. (a) (3 points) lim x ! 3 x 2 x 6 x 3 (b) (3 points) lim x !1 8 x 2 +9 x 4 12 x 2 x +3 (c) (3 points) lim x ! 2 x x 2 4 2. (6 points) If lim x ! x 0 f ( x ) = L; then for every " > 0 , there exists a & > 0 such that j x x 0 j implies
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Unformatted text preview: j f ( x ) & L j < " . Using this denition, prove that lim x ! 2 ( & 4 x + 2) = & 6 3. Let y = p x + 2 (a) (3 points) Use the denition of the derivative to nd dy dx for the function y = p x + 2 . 1 (b) (3 points) Find the equation of the line tangent to the curve y = p x + 2 at the point x = 7 . 4. Find the derivatives of the following functions. Do not simplify. (a) (3 points) f ( x ) = cos(sin( x 2 + x + 2)) (b) (3 points) f ( x ) = (2 x +4) 2 x sec( x 2 ) 5. (6 points) A ball is dropped from a tower that is 128 feet high. It&s position at time t is given by the equation s = 128 & 2 t 2 . What is the velocity of the ball when it hits the ground? 2...
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03_Midterm1-Sample - j f ( x ) & L j...

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