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161E3-F2008 - MA 16100 Exam III Fall 2008 1 What...

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Unformatted text preview: MA 16100 Exam III Fall 2008 1. What approximate value do you get for \/ 4.1 if you use the linear approximation at 4? 2. Evaluate cosh(ln 5). A B C D. 2.075 E. wpow> . 2 . 2.025 . 2.05 2.1 . 2.4 . 2.5 . 2.6 MA 16100 . Exam III 3. Themaximumvalueofx3—3m+9for —3gms2is 4. The minimum value of x3 — 32; + 9 for —3 S x S 2 is A. 5 B. 7 C. 9 D. 11 E. 13 A. —9 B. —1 C. 3 D. 5 E. 7 Fall 2008 MA 16100 Exam III Fall 2008 5. Given that f (3) = 0 and f’(a:) 2 3 for 0 g a: g 3, the largest f(0) can be is A. —9 B. —3 C. 0 D. 6 E. Cannot be determined. 6. If f’(:1:)= a:(a: — 1)2(:1: -— 2), then f has A. 3 local minima. B. 2 local minima and 1 local maximum. C. 1 local minimum and 2 local maxima. D. 3 local maxima. E. 1 local maximum and 1 local minimum. MA 16100 Exam III Fall 2008 7. If f’ (m) = 3(a: — 1)2/3 — 11;, the interva1(s) where f is concave down is (are) A. (—00, 9) only B. (—00, 1) only C. (9,00) only D. (—00, 1) and (9,00) E. (—00, 9) and (9,00) 8- £010 % = A. 2/3 B. 3/2 C. 6 D. l E. 0 MA 16100 ‘ Exam III Fall 2008 9. If f’(:z:) = (a: — 1)(2 — x)(:z: + 3), then the graph of f can look like which one of the following graphs? 10. The graph of f ’ is given below. Only one of the following is true. Which one? 9 y = f’(w) (I: A. fhasalocalminatm=a B. f is not differentiable at a: = c. C. f has an inflection point at a: = c. D. f is increasing for all :1: such that a: > c. E. f(c) < 0. MA 16100 Exam III Fall 2008 11. Find the m—coordinate of the point on the line 3x — 23/ = 2 that is closest to the point (2, 1). 20 15 10 E 8 E 20 T7 10 ' I? D. E 12. Suppose at the point (2, —3) on the curve y = f(:1:), the tangent line has slope 4. If Newton’s method is used to locate a root of the equation f (at) = O and the initial approximation is $1 = 2, find the second approximation m2. A.x2=—1—: 4 B.:1:2=——1—1— 4 C.x2=fi D'$2=% E.m2=g MA 16100 Exam III Fall 2008 13. Find the most general antiderivative of the function g(:c) = cos(2:1:) — 3 sin(:z:). A. 2sin(2a:) + écos(3zc) + C B. gsian) + 3 cos(:1:) + C' C. ésian) — 3 cos(a:) + C’ 1 D. —2 sin(2:1:) + E cos(3x) + C' E. ZSin(2:1:) — $003813 + C 14. If f”(a:) = 1:1/3, f’(8) = 10, and f(1) = 0, then f(0) = ...
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