V63_0121_0020_2008F_Midterm

V63_0121_0020_2008F_Midterm - f ( x ) = x 2-9 x 2-2 x-3 and...

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Calculus 1 Fall semester 2008 Midterm exam This is a closed texbook/notes exam. Use of calculators or other com- puting tools is not permitted. Please use blue books exam sheets as scrap paper, ask the instructor if you need more. All the blue books (together with scrap paper) must be turned in after the exam. Please remember to write your name on blue books. 1. For limits below compute those which exist. For other limits explain why they do not exist. a) lim t 0 sin 3 t 7 t , b) lim x 0 | x | x , c) lim x →∞ x 2 + 4 x - 2 x x . 2. Find intervals of continuity for
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Unformatted text preview: f ( x ) = x 2-9 x 2-2 x-3 and describe vertical and horizontal asymptotes (if there are any) for the graph of this function. 3. Compute derivatives of functions a) x + 2 x 2-1 , b) sin x tan x , c) cos( x 2 + 4). 4. Find all the points on curve y = x 2-2 x +16 at which the tangent has slope 2. Write down equations of these tangent lines. 5. Function y is dened implicitely by equation x 3 + 3 y 2 = 2 . Compute y 00 at point x =-1, y = 1....
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