V63_0121_0027_2008F_Midterm

V63_0121_0027_2008F_Midterm - 4 + sin 2 (3 x ) 5. If g ( x...

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Answer all 6 problems, each worth 4 points, and show all necessary steps on the blue book. Put a box around the fnal answer. 1. Sketch a graph of a function f that satisFes the following Fve conditions lim x m→ 1 f ( x ) = 3 , lim x m→ 4 - f ( x ) = 3 , lim x m→ 4 + f ( x ) = - 3 , f (1) = 1 , f (4) = - 1 2. ±ind the limit lim x 0 sin 3 (2 x ) x 3 3. Di²erentiate the function f ( x ) = 2 x + 1 by taking the limit lim h 0 f ( x + h ) - f ( x ) h and state the domain of f ( x ). 4. Di²erentiate the function f ( x ) = ( x 2 - x + 1)
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Unformatted text preview: 4 + sin 2 (3 x ) 5. If g ( x ) + x sin( g ( x )) = x 2 + π/ 2, Fnd g ′ (0) 6. Let f ( x ) = x-cos( x ). Use the Intermediate Value Theoremn to show that f has a root in (0 , π/ 2), namely there exists a number c ∈ (0 , π/ 2) such that f ( c ) = 0. Note: Must show that all the conditions for the theorem are met. In case you forget, cos(0) = 1, cos( π/ 2) = 0...
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This note was uploaded on 10/25/2010 for the course MATH V63.-0121- taught by Professor Staff during the Fall '08 term at NYU.

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