MATH2 Sum01 MIDTERM EXAM

MATH2 Sum01 MIDTERM EXAM - Summer 2001[A I Midterm No notes...

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Unformatted text preview: Summer 2001 [A] I Midterm No notes, references or calculators are to be used Please show all work. You will not reactive credit if you do not clearly show how you are obtaining your answers. ‘ r / /; .5 ‘ // not allowed. a ‘ (21) um foo) @EW);;_ f (d) m» H; (e) was L (f) 11311 flx) Jflg—E— (g) $.13?“ f(:z)__l__ (h) 31111311135) flag (i) Is f continuous at .1: = 3 (“Yes” “No”)‘ir (j) Is f (w) differentiable at :1: == 3 (“Yesl’j‘or “NO”) 2. Evaluate the following limits. If the limit does not .7 .1 - (egfimdg .Q,g ‘ 6k \ 00¢" K90 mm O» 516 O ‘ X90 . 3—4 (b) £1231 x—2 . lZml WEE =1 9% ii K26 amt Km se the graph to determine the indicated quantities. If a limit does not exist, write DNE as the v wer. For this problem only: no partial credit will be given, and the give-up option is IEIIIIIIII IIESIIIIII III-[INHI- III-III..- III-III..- III-III..- W ? HQ 104w Cm mum/K exist, Show Why. //'\Con'sider the function f (:3) = (x:- 112. i ( Y‘H U l y - ‘ _ a: - ; J Mfl‘ /.. \ X14 :0 1 K7,: I“: Kcl D (a) At what values of :12, if any; does t‘ihe kunction have a removable discontinuity? JU TIFY! 1: WIW Xx 4 ) ii \yw 1: ~13 W l Xxi“ W11 ’ ‘ Anew} y, does thekuncti have a infinite discontinuity? JUSTIFY! ? i m .m (3053 C 4. Use the definition of the derivative to find f’(a:), where f = E and c is a constant. .‘ r .. .. _ - h __ \, W1 mam; urn; .29 5 W m : h e; um \ f w mo Wm :mm gig ;\ WC 1 the curve y = sin(sc2) at the point (fi, 0). @(ffimB 6. A ball is dropped from a tower, and the} height h (in feet) that the ball is above the ground after t seconds is given by ' h: 144 — 161:”. (a) Find the average velocit of the ball from thWfi = 0) to the tWe around. : MM [06?" ‘ (S. ~29 5: g v H i m p d" n r ox 3. \ vns‘\ 1 f Answer: 039}; (b) Find the velocity of the ball at the the ball hits the ground. ’12 “‘\_A »; Oak/theme?! woos—52s t4 . K01” “\qu‘: ._‘ 7. /| ’w 0‘ 3 61 3 lflflflfill III-W3!“- n-Inlll-u ‘ (I) 40M) “%1_; “4 as hoh‘ W? W | 13 “to (b) Estimate the velocity of the objecit at t = 4. 8. Differentiate the following and simplify much as ossible. ’F' I 1- ' ‘F I ~F’Ix “ X-H ? x+2 “5+ 4 , g’ Mr)=(a:+1)3(:r,—I-2)4 I 3 ) (M1) )(Qfi a) Half, / t , “M 3 W” mm m mm {X} 9“ I) (“7-) g + l § L3 my" ( \L 8mm“ ((+ixjm:% x1+<h<+ ! ‘ " K“ 1:643 K” «H ' ' I 2' A 2, ‘ 7' “ L I ‘ xlmxu (m I) 4H><4r><+ Illxbffxij’égifi )i'fz’i'fb’: am How VJW x+)§/+ la + 7.3r MW - . . 12x 44% 42w+rw 5 MH ' . u. (b) Mpg f ‘ (d) f(:c) = sin-(um) + tan(n:c) «PM ; C05(m<3‘n* €60 20170)“ ‘: KIOSK £14K _ 269* Jig (03 ~ Answer: ’FI/K): x x 5m” X4. mum mama/1% l (""m' M) F . i 1 - 1 IE EWle Wacouom [HM “WV X+X1 W Hm, 5i“ “*1 Q9 U.W\ X‘wsg'. Ho! l“ 3 ‘ x'” X‘H-z ' >“’° x C9 \iwb X‘I'Y} ‘ “M 0053-4 @lim J_, )l-jo hm ‘ M; 9—70 sane Wig" 005% , 1 .1 § £321le \‘f 00515 - yum 6MU2056) H 0 x61va ‘ ' 9‘70 6cm? £97!!va sin-1X g - 1m Vha-g)" (3))?” )( RE) i 21mg 6me”+ x3) w -' "—T""-“" 631% 0°15“ . I am “0 c,sz :iWV IV“ mX‘ll 1,. i ‘1" X "' X De+evmmt WW ‘ mfims M mfimwm ov' alISCOYt‘hVIMOwS-W’r ‘ ’me 9mm number. I :Covm‘vmom, 6mg;ng - ‘9 4m = _._&2$_21+ ' ‘ 1,, g X" 1 @ fixh “4"” L} . X‘\ ' Ur yi X= L: Qt'xii' me 01+ x= ' : Is 4‘— viqhi' bowhvmo \t: OOVI'h moms? @5140“, 1m— m L501. hf mtg/whom Lan—(ax‘f 3x’1=0 MM“ “2’ I H ‘i a i I | ‘1 l 1 7 L _ .1; X“? D , ‘K—I X-—‘)1 E._.__um__.xwmz_A5..__£w,w_44m fiaoohsaxfiwlm . _ __ .421». _ n _ “ __._ jmflimaaxl 3.~__.L._9:9___7_-:[email protected]_(1A2§§€fll_u_fi_m .- ' ‘ :mg_;_-__m 5.1.m_(_x—.D . 5"...“er 61_.m.‘£x_:l.)__ u. . m 5 fl 119m: z—Lax H)? t HM INN) ..,. - : - 5‘“ 2 2" I (31H)? h—‘N k. I RE (ZUHOHJ 2)” 2‘— .L— (ax—r0") film i (:2, I . , [Ho /‘ I P I . [A / [ltanHI]:L '2 4— GHOIJ :lll/Vk, .1. [ I I -l/\-‘I0 a ‘ K (annual [2(x+h7+l]1] Z'HWL __L[ I" ( ' I W90 PL h“ ‘- E I (an-Hit)" (ax+2k+l)l] film)»: (W1 ' o (JKHYOMQ'LLH )1 I _l_ 4xi+fixk+ 1+ 2 ' I HST/E [/W :[ J (awn )”(a;«+2h+l )L ‘ ( . z . _ ‘9/2' IQXH) (3X+2l/I+I)L (QXHPHHMHV 8x+%k+¢ —-——~____________v__ (ax-mlfic‘rx “WWII, 3x+4 ‘ (NH)?! : WON}? (3)645} pr q—r .— . «,1 .3. ‘ A; J l ulfirfl- .1.“ ‘ _ H, . 4L?» 1 trrli 51.5; iiii I . [5.4! i: . i , .. .11 , :iu. n: .u..,| . . .. .i. . . . ; : a. ‘ ‘ a , . .. . a . ‘. q{i.1lrJ..J_Lt:l11vw}w1 . . . .1 1 ,... , , .‘ w. . _ . ..- r.‘ f: \ HM: .. u . ._n E . . . H Human,“ p....|.....l.:.r._n “4,411.5... :n..fila...~ .5331: .1133. ASfinSn E 1 1i‘fi5g‘ui4iwla1z i1. 1. ‘ I .. . a , “w z. . . , . ., a . i . . I ‘ r 3337‘“: «9:53.; .Pfinin z? ; ...
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