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161FE-S2005

161FE-S2005 - MA 161& 161E FINAL EXAM SPRING 2005 Name 1...

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Unformatted text preview: MA 161 & 161E FINAL EXAM SPRING 2005 - Name 1. The derivative of f(a:) = secx at x = g is A. g 2 I .. B. W ”7‘) 4 C. g D. 2 E. 4 2 1' i l . \$13?) e—m equas A. —00 B. —1 C. 0 D. 1 E. 00 MA 161 & 161E EINAL EXAM SPRING 2005 Name 3. If f(:n) = tan_1(\/E) then f’(3) equals A. —ﬁ§ B. “75 C. ﬁg D. E. cal: NH A. y=m+21n2—1 B. y=2m+21n2~2 C. y=4m+21n2—4 4. The tangent line to the graph of f(m) = 21n(alc2 + 1) at x=1 is D. y = —2m+21n2+2 E. y: —m+21n2+1 I MA 161 & 161E FINAL EXAM SPRING 2005 Name 5. If y5 — \$312 + 2:1: 2 3, then the value of y’ ( when x=:2 and y=1 is: A. ——1 If?) 2 B. —— 3 C. 0 D. 3 5 2 E. — 3 6. A particle travels along a line with position \$(t) = 2‘. The acceleration of the particle at time t=1 is: ‘ A. 2 2 B _ ln 2 2 v C. (1n 2)2 D. 2 1n 2 E 2(ln 2)2 MA 161 & 161E EINAL EXAM SPRING 2005 Name 7. The function f (II?) = mze‘” has local extrema as follows: A. loc max at a: = —2 and loc min at a: = 0 B. loc max at :17 = 0 and loc min at a: = ——2 C. local min at a: = —2 and a: = 0 D. local max at a: = —2 and a: = 0 E. no local max or min 1+1:2 1—272 8. The function f (m) = is increasing on the intervals: A (—00, —1) and (0,1) B (—1,0) and (1,00) C. (0,1) and (1,00) D ( ,—1) and (—1,0) E ( MA 161 & 161E FINAL EXAM SPRING 2005 Name 9. The function f(\$) = 5\$2—_2\$ has: 2 vertical and 2 horizontal asymptotes 2 vertical and 1 horizontal asymptotes 1 vertical and 2 horizontal asymptotes 1 vertical and 1 horizontal asymptotes wuowr 1 vertical and no horizontal asymptotes 10. The function deﬁned by . ‘ f(:1:) = .722 for :1: <0, f(\$)=\$+2for0§\$§2,and f(:1:) =4+ln(:1:— 1) fora: > 2 has discontinuities at: A. no values of x B. X20 and x=2 only C. X22 only D. x=0 only E. x=0 and x=1 only MA 161 & 161E‘ FINAL EXAM SPRING 2005 Name 11. The function f(x) = 23:3 — 3x2 — 12a: is cbncave up on the intervals: A. (—00, —1) and (2,00) ‘ B. (—1, 2) 1 C“ (—0015) 12. The base of a triangle increases at the rate of 2 in/min while the area increases at the rate of 6 in2 / min. At what rate is the altitude of the triangle changing when the altitude is 2 in and the area is 4 in2? A. 1 in/min B. 2 in/min IC. 3 in/min D. 4 in/min E. 6 in/min 13. Estimate tan (3%) using differentials near a = E. ' 24 _ 7r .14. Determine how many critical numbers the function f (:12) z: 11:7 + 14:1: has. A. none ‘B.1 C3 D5 E6 15. The absolute maximum and minimum values for f (:17) = 11:4 — 811:2 + 1 on [—1, 3] are respectively ' 16. If f”(a:) = (m + l)2(\$ — 2)\$3 then f has inﬂection points with :L‘ values just at A. {4,0,2} B. {—1,2} 0. {—4} 'D. {0,2} E. {—1,0} 17. Suppose that f (m) is continuous on [—1, 3] and f’,(\$) exists on (41,3) such that ~2- g f’ (m) g 4. Which one of the following is always true? 10 20. If f(a:) = \$4 + a: + 2 and \$1 = 1 then 332 from Newton’s method is (77‘) 1 21. If f’(a:) = 1mg and f (0) = 2 then determine f (1) 12 pd?» .0 .U =1 cowl: >J>~l>1c> *‘Ia F11 2 5 5 4 22. If/ f(a:)da: = 3, / f(a:)da: = 4, and /4 f(a:~)da: = 6, then /2 f(a:)da: equals 1 1 23. If f(x) = /1 4 t4 +t2 dt then f’ (2) equals 13 ‘A.0 B. 4 C. 2 D. —2 E. —5 A. 2 B. 4 C. 6 D. 8 E. 16 4 24. / x(S\/E+ 4)d2: equals 1 25 /3 d2: eual ' 2 (2x—3)2 q S 14 A. 24 B. 36 C. 42 D. 92 E. 108 .U .0 P3 P ODIHOWINHUII-ANIOO H ...
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161FE-S2005 - MA 161& 161E FINAL EXAM SPRING 2005 Name 1...

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