Practice_exam3 - Math 2250 Spring 2011 Practice Exam 3 Use either the first or second derivative test to find all local minimum and maximum

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Unformatted text preview: Math 2250, Spring 2011, Practice Exam 3 Use either the first or second derivative test to find all local minimum and maximum values of the following functions. 1. f (x) = x2 − 3x + 2 2. f (x) = xex 3. f (x) = x − x2/3 4. f (x) = x−3 x+1 Curve sketching: Suppose that f (x) is defined on [−3, 3] which satisfies the following properties: 5. • • • • f (x) f (x) f (x) f (x) is is is is increasing on the interval [−3, 0], decreasing on [0, 3], concave down on [−3, 1], and concave up on [1, 3]. Use this information to sketch the graph of f (x). 6. Find all horizontal asymptotes of the function f (x) = 2+x 3x − ln x on the domain (0, ∞). 7. One of the following functions has a vertical asymptote at x = 0. Which one? sin x a. f (x) = cos x b. f (x) = sin x x c. f (x) = x ln |x| d. f (x) = x + 3 x2 + e x x + 4 x2 Use Riemann sums to approximate the following definite integrals. 4 8. (2x + 3)dx using 4 rectangles and left endpoints 2 2 (x2 + 1)dx using n rectangles and right endpoints. Write your answer in summation notation. 9. 0 10. Take the limit as n approaches infinity in the above expression to obtain the value of the 2 (x2 + 1)dx. definite integral 0 1 You may use the following helpful formula: n i2 = i=1 n(n + 1)(2n + 1) 6 Solve the following definite integrals: 4 11. (2x + 3)dx 2 π/2 12. (2 sin x + 3)dx 0 4 1 dx 2x + 3 13. 1 1 ex+2 dx 14. −1 Solve the following indefinite integrals: 15. (2x + 3)dx 16. (sin x)(sin(cos x))dx 17. (x ln x)−1 dx 18. xex dx 19. xex + ex dx 20. √ (sec2 x)( tan x)dx 21. x dx x+1 2 2 2 ...
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This note was uploaded on 12/10/2011 for the course MATH 2250 taught by Professor Chestkofsky during the Spring '08 term at University of Georgia Athens.

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Practice_exam3 - Math 2250 Spring 2011 Practice Exam 3 Use either the first or second derivative test to find all local minimum and maximum

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