Sol-165E3-F2004

# Sol-165E3-F2004 - ”’ NAME GR m E.‘ I MA 165 EXAM 3...

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Unformatted text preview: ”’\. NAME GR m '_ E.‘ I MA 165 EXAM 3 Fall 2004 Page '1/4 STUDENT ID RECITATION INSTRUCTOR‘ Page 4 _- RECITATION TIME ' TOTAL‘ V /100 DIRECTIONS 1. Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages'2, 3 and 4. 2. The test has four (4) pages, including this one. Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. ‘ 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this exam. 9-" 1. Find the absolute maximum and absolute minimum values of the function f = ﬁ—l on the interval [1,2]. g1(x)__ (x+L)1—X11. _ ’L (H if- ’ bx + 07‘ g/(x) 2 O r. 1 m2 :: 0 W0 Soils/330“ 2. Explain why the function f = 2:2/3 does not satisfy the hypotheses of the Mean Value Theorem on the interval [—2, 3]. §/C¥)=%X'% Vim" x¢o ; Mo) DNE {Kn not 4m“ xe(__2;5) , 3. Use calculus to ﬁnd a positive number such that the sum of the number and its reciprocal is as small as ossible. Lﬁt 321+; ) 743'“??? ‘7? dgroi X'LaO—aX=L® W. ﬂ- rlo \$ OJLS. mini MA 165 ‘ EXAM 3 ' Fa112004 ' Page 2/4 Name: . ' v . ' ‘ . ‘ - ‘ ‘0 credit. i} anyway—in @Yfe'tt Mam ‘73 M Work ov'wovk I . 4. Find each of the following as’a real number, +00, _——oo or write DNE (does not exist). — ’ - x ox ew+e ‘” —_2 ﬂ QM, e’iz *‘._L_’HL'M 31.9. :2, :1 x—ao ‘ 2.x xv-‘O 2. 2' .0. o ‘ ~ 9- . (a) ll—IR) \$2 0 - ;_ r. - __-_i_.___,l . (b) lim sm lmél-iQ/gm V5317“: : 1- w—rO :17 ' Xao ’1- ,0, . O , C lim x—\/m2—1 :L'm X-m)(x+ﬁ) ()HOO(' ) x-’,°°( ' 094311) 00—00 9— ' 7. 3—90? X-P 3‘24 x4” m x“ E, l V» ((1) lim (1+flc)1/“c :X/{m 6&0”) ':1j\‘m €§£”(\+x)__ 0'", ermine) + + z—+0 x90», ’ xﬂ’o‘k e x—gﬁ X gm anx) 5,14% 71;: ’0" I Um (hr-x): : (14) 5. The numbers 3 and —1 are critical numbers of the function f = 2x5 — 5x4 — 10:133. Showing all necessary work, decide whether f has a local maximum or a local minimum (a) at 3 using the ﬁrst derivative test, I . . ca) 4 (x) = 107:“- mud—30 x“ = 10x2(xq’-2.m..3): ' 4 ' = ioxzam'e—e ® :1 . / 0 O -— _ ___..0-\-++«'+ ; W £00 ’1 0 3 s: E, Mm neﬁqxive “(’9 Positive ox 3 C23 " I ind-m Ni. . i lerle a, doch w u 10C. min. @ (b) at —1 using the second derivative test. g”(x) -_-: 4093—60 x‘aww ® Wu) =4o(..f-eo<—o‘—[email protected] <9 _, _40 :6 O +60 <0 «Local mxu‘mekwai 1- MA 165 EXAM 3 Fall 2004 Page 3/4 Name: 1 (16) 6. Let f(m) = 1+e_m function on the axes below. Give both coordinates of the intercepts, local extrema and points of inﬂection, and give an equation for each asymptote. Write NONE where appropriate. . Give all the requested information and sketch the graph of the in Mite. 6‘6? X domain sérwrm” IIIEHHIIIID . a, __ . , - - ' hm ire-x = " “3:0 1/) Wk symmetry N 0 N E - 61> X—a -"0 .X ' - ’ I — "" SEX) : 2:21;)?- 1(——&)7 horizontal asymptotes x4 __ 1, ) ‘3 -— U @ : e‘x )2 vertical asymptotes N O N E (1+e'x gin {out 0‘1 (“‘5‘”) ) hC;l-E:O:L;qn;:3401:\$éo£ Min. intervals of decrease N0 N E (D I; _ . «to : a we“) ee‘L—Jég—L‘ 2f 195‘“ max‘ma N o N E ) -X _(l+e_'1)€f:‘ +Qe-xe—x local minimal; N0 N E j (9 — “+6393 intervals of concave down (a go a; -€”‘—e’2x+2e'2" ’ > 4 7x 3 . A ( +e ) intervals of concave up r (.00 )0) ‘I Q) ﬂ. (My, ofinﬁectionmm© 5 " '0 l MA 165 EXAM 3 Fall 2004 Page 4/4 Name: (14) 7. A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and .CB. Find the maximum capacity of such a cup. v- A B \/ 1 Trvzl’i. @ R z (6) 9. Find f(x) if f’(a:) = 25ina: + sec2\$ and f(0) = 3. i”) = -‘2Losx +tomx +C, G 1 {1(0)=——2c.o50 +tan0 +C 3 :: X \I 8 8 5 (5) 10. If/f(a:)da:: 1.7 and ff(a:)da:=2.5, ﬁnd /f(a:)da:. 2 5 j25f(y)oix t: S:§(x)d’x -—- f:'§’rx)d7r : 1,7 «2.5 2—0.2 ' - ' 9 E53 ...
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Sol-165E3-F2004 - ”’ NAME GR m E.‘ I MA 165 EXAM 3...

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