161FE-S2004

# 161FE-S2004 - MA E Name Recitation Instructor FINAL EXAM...

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Unformatted text preview: MA 161 86 161E Name Recitation Instructor FINAL EXAM SPRING 2004 Student ID number Div—Sec Recitation Time Instructions: 1. 2. 3. Fill in all the information requested above and on the scantron sheet. The exam has 25 problems, each worth 8 points, for a total of 200 points. For each problem mark your answer on the scantron sheet and also circle it in this booklet. Use a number 2 pencil on the answer sheet. Be sure to ﬁll in the circles for each of the answers of the 25 exam questions. . Work only on the pages of this booklet. . Books, notes, calculators are not to be used on this test. . At the end turn in your exam and scantron sheet to your recitation instructor. MA 161 & 161E FINAL EXAM SPRING 2004 Name 1. The tangent line to f(a:)= 32 atx=2is A 2 +6 a:+2 '9 a: B. y=2\$+4 C. y=——8a:+8 D. y=—2a:+12 E. y=8x~8 2. W equals A_ 0 B. 1 C. —1 D. 2 E. —2 MA 161 & 161E FINAL EXAM Name 3. If = ln(ac3 + 2552) then f’(2) equals 4. If ysinac + (Using = 20, then y’(ac) equals SPRING 2004 A. 5/8 B. 41n16 C. 5/4 D. 10/3 E. 81n16 —(y sin ac — cos ac) A. _ (sm y — y cos ac) B —(y cosac + sing) I (sin as + as cos y) C —(ac siny + cosy) ' (sin a; + :1: cos y) D —(y sinac +cos ac) ' (siny + ycos ac) E —(ac siny + cosy) (cos as + as siny) MA 161 & 1_61E FINAL EXAM SPRING 2004 Name 5. If f(x) = tan—1(2x) then f”(x) equals —4\$ 6. If f(x) = sin(1re“‘/2) then f’(0) equals A. O MA 161 & 161E FINAL EXAM SPRING 2004 Name 7. Find the absolute minimum value for A. 2 f(a:) = 2:3 —— 33: on [—3, 2]. B. _2 C. —1 D. —20 E. —18 8. The largest interval on which f(a:) = —2m3 + 33:2 + 123: is increasing is MA 161 & 161E FINAL EXAM SPRING 2004 Name 2 _ em — e4 9. 11m m—)2 (I: — 2 equals A_ e4 B. 264 C. 64/4 D. 864 E. 464 2 10. / |:1: — 1| d3: equals 0 A. 1/2 B. 2 C. 3/2 D. 1 E. 5/2 MA 161 & 161E FINAL EXAM SPRING 2004 Name 3 :1: 11. d9: e uals /0 Va: + 1 q wloo .6 .o w 22> wlmwlpkh‘wlw F5 1 12. / (1 + m2)2dm equals 14 o MA 161 & 161E FINAL EXAM SPRING 2004 Name 13. Let f(a:) = 51:3 — 51:2 + 2:1: + 1. If 51:0 2 1 then the ﬁrst approximation, :31, to a root of f using Newton’s method is A. 0 B. 1/3 C. 2/3 D. 4/3 E. 2 14. Determine the number of vertical and horizontal asymptotes for :34 A. 1 a: : ———. f( ) (51:2 — 1)(:1:2 + 4) B_ 2 MA 161 & 161E FINAL EXAM SPRING 2004 Name 15. If f’(m) = 2303 + a: and f(0) = 4 then f(2) equals A. 14 B. 12 C. 24 D. 18 E. 25 b 16. Determine b so that f = m2 + 50—3- has an inﬂection point at a: = 1. A.1 MA 161 & 161E FINAL EXAM SPRING 2004 Name 17. Determine a so that 5 + a: if a: _<_ 0, f(m)_{\/m2+a ifm>0 is continuous at a: = 0. 18. Let f be a continuous function such that 1—m2§f(m)31+m2. ?> u |—| 1__1 |__| 1 Then / f (m)dm must be in the interval 0 v .5 U31 0 l—II—-ﬁI—ﬁr'_—I H ODIN cold: 1__.1. I EIJ r——I “l—l 10 MA 161 & 161E FINAL EXAM SPRING 2004 Name 19. Let :1:2+4:1:+1 if:1:<0, ﬁx): { :1:2—2:1:+1 ifmZO. Which of the following statements is true? A. f has a local minimum at :1: = 0 B. f has an inﬂection point at :1: = 0 C. f has a local maximum at :1: = 0 D. f is discontinuous at :1: = 0 E. f is differentiable at at :1: = 0 (I: 20. If/ f(t)dt = 2:4 — 3:1:2 + :1: for all :1: then f(1) equals 0 wwow.» actor—Io 11 MA 161 & 161E FINAL EXAM SPRING 2004 Name 22. A kite is 100 ft above the ground and moves horizontally at a rate of 10 ft /sec. At what rate (in radians /sec) is the angle between the string and the ground changing when 200 ft of string has been let out? A. —1/10 B. —1/20 C. —1/30 D. —1/40 E. —1/50 12 MA 161 82: 161E FINAL EXAM SPRING 2004 Name 23. A box with an open top is constructed from a square piece of cardboard 5 ft. wide by cutting out a square from each of the four corners and then bending up the sides. The box is then ﬁtted with a lid cut from a second piece of cardboard. Assume the length of the sides of the squares cut out is 23. Find the total surface area of the box, including the lid, as a function of m. A(m) = A. 50 —— 20\$ B. 50 — 10:1: — 3:132 C. 150 — 12023 + 241:2 D. 150 — 603: + 6952 E. 50 — 10\$ 24. Let g(m) be a differentiable function on (—00, 00) such that 9(5) 2 —5 and 9(6) 2 3. Which of the following statements must be true? I. There is c in the interval (5,6) with 9(0) 2 8. II. There is c in the interval (5,6) with g’(c) = 8. III. There is c in the interval (5,6) with g(c) = 0. A. JustI B. Just I and II C. Just I and III D. Just II and III E. All three 13 MA 161 & 161E FINAL EXAM SPRING 2004 Name I 25. The largest area of an isosceles triangle that can be inscribed in a circle of radius 1 is A. 1 B. g7? m C- T Notes: You can assume that \/§ 2 1.73 and 7r 2 3.14. An isosceles triangle has two sides of equal length. 14 ...
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161FE-S2004 - MA E Name Recitation Instructor FINAL EXAM...

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