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Unformatted text preview: Math 242 Final Exam, Spring 2011 Sections 012, 014, 050 NAME: There are 12 questions on 12 pages . The points per page are 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6. The 13th page has some formulas you can refer to if needed. [5 points] Question 1. Evaluate the limit. lim x →∞ ln ln x x 1 Question 2. Let R be the region bounded by y = cos x and y = 0 between x = π/ 2 and x = π/ 2. [2 points] 2a. Find the area of the region R . [3 points] 2b. Find the volume obtained when R is rotated around the line x = π/ 2. 2 [5 points] Question 3. Evaluate the definite integral. Z π/ 2 cos 5 x dx 3 [5 points] Question 4. Evaluate the definite integral. Z 2 √ 2 1 x 2 √ x 2 1 dx 4 [3 points] Question 5a. Evaluate the indefinite integral Z 1 x 2 5 x + 6 dx . [3 points] Question 5b. Evaluate the definite integral Z ∞ 4 1 x 2 5 x + 6 dx . 5 [6 points] Question 6. Use EITHER the Trapezoid Rule OR Simpson’s Rule to approximate the given integral using the specified value of n ....
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This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.
 Spring '08
 wang
 Formulas

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