Sol-165E3-F2001

# Sol-165E3-F2001 - MA 165 EXAM 3 Fall 2001 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 3 Fall 2001 Page 1/4 NAME erlaclzn} k8 STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, recitation instructor" I ' 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. . 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. nub-C»: (10) 1. Find the absolute maximum and absolute minimum values of _f(:c) : 3:3 — 3.1:2 + 3.1: on the interval [—1, 2]. J; (—4) = —- 7 ' :axi—ex + 3 o : 3(x‘—-:Lx+t) 3L'x—IJQ’ H3): 9— 9 CD abs. max. Ll'EI-S x1! LCYI+LCmQ Value) abs. min. t . C9 (8) 2. Suppose f is continuous on [2,5], f is differentiable on (2, 5) and 1 S f'(:c) S 4 for all z in (2,5). Show that 3 S f(5) — f (2) S 12. (Hint: Use the Mean Value Theorem.) 3 his : £C5)"Ra’) {:ov SW C I" (1:5)_. 6’— 9» t I f 'CLSI)_"R2‘) i H. Because. 1‘5. F0054 5‘—-9- ' am. ’XIACQJS'J- 135 . .1 3 f. RSV-Huge. 1a. MA 165 EXAM 3 Fall 2001 Page 2/4 Name: Fw #34; :1 TE ans. Is WOWETS ﬁv m 5°;*T‘3_ji__ (20) 3. Find each of the foilﬁwing limits as a real number, +00, —-00 or DNE (does not. exist). , Sims—2: gym QOS’x——f H [gym -—Smx a 11m : 2 ()”‘*D 333 x—ao 3x1 an 6X ' (b) lim mn—l“: \ _z—}l+ 1 (C) lim xtan — Iii-'91:!) I Fox): xex+ ex 21.” {30;} = 'L”‘+')€’K ﬂ , 2c X I Igvvxé—I “rs :xe+1€ Nd“) E413 i am "4. *' JP'CXIVO W" 7" L ,{3‘ (-I) =-C 3.6, ' ._ 31E} 2 e“ = “i” LQCaQ Minimum - MA 165 EXAM 3 Fall 2001 Page 3/4 Name: 2 20 5. Let f 2: = . Give all the requested information and sketch the graph of the 1:2 -— 4 function on the axes below. Give both coordinates of the intercepts, local extrema and points of inﬂection, and give an equation 01' each asymptote. Write NONE where appropriate. ' ' - - Symme‘lv7 {:(“xl : {:0} x—9‘3mx1vq ‘ x—Mo I—q/xa. '1 x at; =LX~1)(X+L)=O X a 6L 357mlolales- - _. 1. —3x £mrkx Hllx Xlx_ 1 ‘ CVITlc-‘Q FT X=O}y’:o. -W“”ll"9 *- SKA-(Wais- ' ?(3XZ+LU _ 1 Ln 3 ¢ 0 horizontal asymptotes -— _ - I] X “' ' ' o _ - O .52 - - - F l < (0,0) Lt: vertical mymptotes x ._ Q. o (I x =I,___I a. . \ ‘\$ (X) 0 “E X40 Lino”. intervals of increase _ FIG“ O H, (632\$) Pinko ﬂ X z ‘9" av X 7 a . . . ' I ._ C Can-Cu we ml”)— local. “mum t 'l :11th O h? _1< X4- 1 intervals of concave dom1| C‘, Q.) J _ l CCU“ Ca. we add intervals of concave up (_ 0'0 L1) 00) ® {. I points of inﬂection N o M _§ CD MA 155 EXAM 3 Fall 2001 Page 4/4 (12) 6. Find the dimensionspf the rectangle of largest area that has its base on the :c-axis . and its other two vertices on the parabola y z 8 — 3:2. A: 31ng a; :‘E'HX A=3x( e—Xl) -_— lexuaxi wm- 05x5 I? dA _ _ ’— 23; y ’6’ w: (Take; oﬁm H? O I: "9ng _ M We 3615 MISSM . (5) 7. Find the most general antiderivative of f (I) z 4seca: tans: — EB I! i! _. Take 0*; LE I? C 15 104551ng H‘Secx—aﬂnlxl + cj SETS (5) 8. If 8 ﬁzz-M2: = 1.7 and 8 f(:c)d:c : 2.5, ﬁnd 5 f(x)dz. I 8, f2 5- f5 L M ,‘é_q-ngw is Wmh¢3.tb‘:-|t gram-:lemébx 4810:1424 “W ' ‘9 :L 1 .5“ 0. sub: (getl'aﬁn 4W a # (10) 9. Find f if f”(z) 2 J5, f(1)= 1, and f’(1) = 2. ...
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## This note was uploaded on 09/14/2011 for the course MA 165 taught by Professor Bens during the Fall '08 term at Purdue.

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Sol-165E3-F2001 - MA 165 EXAM 3 Fall 2001 Page 1/4 NAME...

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