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1271Sol_final3 - —-— 6 12am-~-2 1 Which of the...

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Unformatted text preview: —-— , ' , 6) 12am -~ -2 1. Which of the following is NOT equal to /O x/4 — xgcim? ” 2 . —_ _ - 2 A. 11151301.; n 4 (21) /n2 B. 7r C. F(2) — F(O) where F’(:c) = V4 - x2 71—1 2 E. Rhino .2 5V4 — (202/712 1 // 7 S Livy” VL" 'L/ ‘// . 2 o l 1.2.” Suppose that the function f is continuous and differentiable on the closed interval [—1,2]. Assume that f(—1) = —-5 and f(2) = 7. Which of the following is NOT true of the function f? A. f achieves an absolute maximum on the interval [—1, 2]. B. There is a point c in the interval [—1, 2] where f(c) = O. C. There is a point c in the interval (—1, 2) where f’(c) = 4. D. The above statements must all be true for f. @The above statements can all be false for f. gymhich of the following describes the set of real mimb ers on which the function “33) = ln(l + x2) is concave down? A.O<:I:<1 .113’>1 C.—l<x<l ffny 1 2X D.x<-—1 14 x1 E.$>l I f (x) —, 1W)": 10’9””) .911» I+k" ll _. f _ )9 W -I I f\ (/ m f sins: 4. Evaluate/(cosxfi dill LL: WK A' §(COS$)._§+C 56% : - 9/4 x M B. %(cosx)%+C 3 @§(cosx)§+0 Sffix 1X: _. I‘M D. —g-(cosx>% + 0 (mm B. . _2 ~§(sm:c 2- + C "5. The difference of two numbers is 20. What is the smallest possible value for the ”product of these two numbers? A. —100 ‘ :10 t” ': ‘ 13*240 X3 > a X20 0—400 minimize x3 13.100 E240 Fm”: x1-wx fl“) : 1X—2.a Xz/O ,. ‘l /1__ _ @ztEvaluate lim “in—3:. f » 1'—*‘8 2+:c5 6—2 ‘_ x 5 3 B. 00 a w i '2 + X”; (1—00 X»)»& D. f4 ‘, E 8 ' a m 1/44. Z 3 KI/s Z: “a K“) '3) J X‘2/‘5 y¢,-a7 2 (7K 3 - L : 3 / __ ' 2 2 3 7 The area of the region lying between the curves y— — 22:»:1:2 and y — to which of the following? A. 2 B. 9 C. 4 D. 27 wwwwwwwwwwwwwwwwwww 1 @ 9/2 —~:r is equal 1x 3X**’ '5 '5(3X-K1>6{X 0 I ’ timest=0andt==313: 0% meters per second . T52 meters per second C 11411(4) meters per second D.» —-9 meters per second E. 4— meters per second U,“ : say—3C0) 3 _,’-_l 1 2 ‘4 — - “‘ Problems 9 and 10 refer to the graph 3/ 2 means that the function’s value is not the means that the function’s value equals the height of that circle. f(LL‘) depicted above. An open circle height of that circle. A solid circle 9; The number of values a in the interval [—8, 8] for which lirn f(a:) does not exist is: Al \¢/ 1. .2 ) I (3.3 D4 E. 5 or more 3 Kill” f’ is the derivative of f, then f’(a:) < 0 when: A.:z:=——6 B.l<:1:<2 C.:c=4 @sc>6 E. none of the above 11'1'1If flag) 2 e31" — 6‘3“”, then what is the 1271th derivative f<1271)(av)? A. 31271f(33) B. 638139; __ e—3813m C. 31271f(—CZI) D. 1271f<1270>(:c) @31271(€3z + e—Bx) 12 The derivative of the function f(t) = 1n(ln(ln t)) is: 1 A.— , t ’ L“, i... 3—1— f({"r”6n(w> M Int 1 tln(t)1n(1nt) 1 1n(1n(1n 2%)) 1 tln(t)3 D. E. 13. If f(x) = Axum/Wait then what is f’(2)? A. O B. §(64—11\/1‘1) C. 1 D 2m @12 f'(k) : (KM) c/ 7+/M/)l f’m ":- s {/7 + 6i :11 . 1 14. If f(x) = VHS/“:6: then If(:1:) ~11 < 1% for all :r > N if A.N=—10 B.N=lO. CNZ—IOO. I 61’”po ’ \I < _ ,( v, _- aN=100 )p(x3 [0 } K) > K0 EN=rla II if”) < ‘“ * far) > 3 ’0 , I!) /0\/7+/0<1//7 ; mfi+l0>qu V7 >/«7 J7 >m/u / X > mo A. B D. E ~73?! stem/y + y2 ' yew/y __ y2 my ' er/y — y2 y 2 E _ 2731261731 year/y + y2 xem/yl— y2 . d 15 If (ax/y = :L‘ + y, then What is Fig? $2+xy+y2 :figfi‘A television camera is positioned 4 kilometers from the base of a rocket launch" ing pad. Suppose that the camera is always aimed at a rocket, and that the rocket moves straight upward. If 9 is the angle of elevation of the camera, then 6 = 0 when the rocket is on the launch pad, and 6 increases as the rocket rises. (1) Express tan(<9) in terms of the height of the rocket. (ii) What is cos(6’) when the rocket is 3 kilometers off the ground? (iii) If the rocket is rising at 500 meters per second when it is 3 kilometers high, then how fast is 6’ increasing (in radians per second) at that moment? Express your answer as a fraction in lowest terms. 0L) {am (9’ : .13- 9‘} 7 “I ix, l / l I” g) If L133 ‘> ./ 6" “f; x : awe :3' Likm :90007w ‘7 Wfi&:§q ”(km/£¢( I / l)(3000) : $00 m/$€c/) @{UF 6"(11’) 1 ? 243) :5 J,— fi'“) fly“) u, 596%? / 9;;- 975‘) : l— L :9 10 I 4/ )— -1 1?. Estimate /_1(5:c2 + 1)da: using a Riemann sum with 5 subintervals of equal length. Use the left endpoints of these subintervals for your sample points. Express your answer as a fraction in lowest terms. AX: 3: l—+—+——+—-+-'l 9 X0 : " X4 1 '15‘31 : —E_ 5" 5’ )(1 "s “I +1"! e ‘ I 5 ” 3 X5 1 “I 4 E _ 1 5' E K : _ L, l l. g :_ .15 L — 3 5— 5' ’ (5"va )4 + A A “”3 W h V‘H- llve ,. W! V’ N N + ‘4" I \1 Q ”UN VHN 11 18. To make a doughnut for breakfast, rotate about the y—axis the disk bounded by (x — 7)? + 3/2 = 9, centered at (7,0). Write a definite integral that gives the volume of your breakfast. Evaluate the integral (but don’t eat the doughnut) . 12 :19. Let f(:v) = I(x2—9x+15). Find the absolute m values attained by f on the interval [0, 7]. these extrema is attained. aximum and absolute minimum Determine the m~values Where each of : 3K -/y)( HS’ -, 3(x1~4x +3’):"5(xez){x~r) m a < 3,“) X : I $‘ X ': :2 13 20 Estimate {3/664 by the method of linear approximation, using the fact that 43 = 64. Be clear about which function you are linearly approximating and what its linear approximation is. At the end of your calculations, express your final answer as a single number in decimal notation. I 2/ (6(1)’ a :17? (K) : L X- 3 / 64*:sz 3 2.('/:_L/‘) /a ’>: LU): £(LL!) + (6‘!) (X'Wl 3 97:49) 2 “(I M W 2 £1 L 2‘3 : L/“ La : 9+ L: 112? 5.737 10 14 21;”"Write an equation for the tangent line to the graph of y 2 xcoswx) When 33 : 3. 3': XWN"(‘$;A(/M}fié¢x+4flig ’ - J. ~_’}¢VJ W 3 (s 7 _ I 3(3) 3 “WWW 9‘5 r "#:12/ 15 ...
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