211-2007&2008-2-F10-May 2008

211-2007&2008-2-F10-May 2008 - Kuwait University...

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Unformatted text preview: Kuwait University Math 211 May 29, 2008 Dept. of Math. and Comp. Science Final Exam Duration: 2 hours Calculators and mobile phones are not allowed. Answer all of the following questions. 1. (2+2 pts.) (a) Find the Maclaurin series of f ( x ) = x 3 e x/ 2 . (b) Using part (a) find the sum of ∞ X n =0 n + 3 2 n n ! 2. (2+2 pts.) Let f ( x,y ) = x 3 y- xy 3 x 2 + y 2 , if ( x,y ) 6 = (0 , 0) , if ( x,y ) = (0 , 0) (a) Show that the function f is continuous at (0,0). (b) Use the definition of partial derivatives to find f x (0 , 0). 3. (2+3 pts.) (a) Let y 2 z = sin( x + 2 y + 3 z ). Use implicit differentiation to find ∂z ∂y . (b) The surface S is given by xy 2 + z 3 + sin( xyz ) =- 1. Determine whether the point P(1,2,3) is on the tangent plane to the surface S at the point (-1,1,0). 4. (4+2 pts.) Let f ( x,y ) = 1 3 ( x 3 + y 3 ) + x + y and the region R = { ( x,y ) : x 2 + y 2 ≤ 2 } ....
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211-2007&2008-2-F10-May 2008 - Kuwait University...

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