102-2008&2009-1-F10-January2009

102-2008&2009-1-F10-January2009 - K u w a i t U n i...

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Unformatted text preview: K u w a i t U n i v e r s i t y Department of Mathematics & Computer Science Math 102 22 Jan 2009 Calculus B Final Exam Two hours Calculators and mobile phones are not allowed in the exam. 1. Let f be a one-to-one differentiable function such that f (2) = 3 ,f (2) = 5 ,f (3) = 4 . If g = f- 1 , what is g (3)? [2 pts] 2. Show that if f is one-to-one, then g ( x ) = e f ( x ) is also one-to-one. [2 pts] 3. Show that if cos(arctan a ) = tan(arccos a ) , then 2 a 2 = √ 5- 1 . [3 pts] 4. The figure below shows the graphs of the polar equations r = cos θ and r = sin2 θ . Find the area of the region that lies inside both curves. [4 pts] Minus 0.5 0.5 1.0 Minus 0.5 0.5 5. A curve C has parametrization x = 2 t 3- 6 t ; y = 2 t 3 + 3 t 2 , where- 1 ≤ t ≤ 1 . Find the coordinates of the points on C at which the tangent line has slope 1 / 3 . [3 pts] 6. Find the arc length of the curve C whose parametric equations are [3 pts] x = ln p 1 + t 2 , y = tan- 1 t, t ∈ [0 , 1] 7. Evaluate the following integrals:7....
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This note was uploaded on 02/23/2010 for the course CAL B 0410102 taught by Professor Deparpment during the Spring '10 term at Kuwait University.

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102-2008&2009-1-F10-January2009 - K u w a i t U n i...

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