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Unformatted text preview: Math 202 Final Exam Spring, 2009 Part I Do all parts of the following five problems. (1) Compute the derivative dy dx for each of the following (15 points) : (a) y = x x + x 2 ; (b) y = 2 sin( x ) + e 2 ; (c) y = arctan( e √ x ) . (2) Compute each of the following integrals(30 points): (a) Z 2 x + 1 x 2 + 5 x + 6 dx ; (b) Z x 2 p 9 x 2 dx ; (c) Z e x sec 2 ( e x ) dx ; (d) Z 2 1 √ x ln( x ) dx ; (e) Z π/ 4 p sec( x ) tan( x ) dx. (3) Compute each of the following limits (10 points): (a) Lim x → e x 1 x 1 cos( x ) ; (b) Lim x → sin(3 x ) 1 e 2 x . (4) Compute the area of the entire region between the two curves y = x 3 3 x 2 +2 x and y = 3( x 1). While your answer should be numerical, you need not combine the numbers you get. (Hint: It is helpful to sketch the curves.) (8 points). (5) Sketch the curve given by the equation r = 1 sin( θ ) in polar coordinates, labeling the x and y intercepts, and compute the area it encloses. (7 points) 1 Part II Do all parts of three out of the following five problems (10 points...
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This note was uploaded on 10/29/2011 for the course MATH Math taught by Professor Ocken during the Spring '11 term at CUNY City.
 Spring '11
 Ocken

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