MTH132-Test1-Sol - Page 1 2008—9—12 Name (Print...

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Unformatted text preview: Page 1 2008—9—12 Name (Print Clearly): Student Number: MTHl32 Section 5 & 18, Test 1 Sept 15, 2008 Instructor: Dr. W, Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [4 pts each]. Find the following limits. x/x2+2—x +x—l «,m a, (a) lim x—>O x2 Page 2 2008-9-12 2 [5 pts each]. If (x) 2 1/4; , please evaluate the limit of the form gnaw , ti. My) y “a {r l i? ‘3 V m {it f A ‘ :V I w»~A-_*M“*Wm'mmm’m w e ‘ mum-w» f "I 9 , r, r ,. .c '. awn} 2§R§54L1Wi1 lit?- “w 1151 3 [10 pts]. Please use the intermediate value theorem to show that the equation cos(2x) — Zsin x = 0 has a solution. Page 3 2008—94 2 x2 — 3 4 [5 pts each]. Suppose y = —— . x — 2 (21) Find the asymptotes of this function. ? ,7 Q ., e» "T? g . .Miww“:“ “:4 3% "5* \”““‘°”*‘*%’*‘ W 7“: J' :1 AM» in“ i v : “W WM 5 (b) Find the dominant terms and sketch the graph of this function. ., .t < « . a 3 W M 5 w, v 2' p {I}: 3 M3? ~3- m‘ffi WM; ,9; -~§~ if) N ,«g’g‘pvmgmzflw “‘E‘fii rm. 5 W; 33 ~17 2m 5 i “‘3?” 11* gr” i m ’5 J? a 4 ‘ ‘ v A . 4 w , u -. w “W” W “v , 1 t ' 1"” MM ’5 2*; W??? ‘” . Heow fii-‘J’ih’ mite” igfflfi‘ i 3 “3623; j. A z” ._ gm.“ r1 k x‘: \. , a 5 , a «4L VI A“ 9 I N is“ 1% w {11% “:a "“a c ‘* 3 2V “:2 V , “V” ’ i a f g Us :3: mix .2 :3! was». w. “ v? ' W Now (I; s r We». " “I \t ,Xfixf‘ K 9.7 (x 1 ix“ , :y “3; {xi ,,.§._ 3 Hamil «J m «é» “3 .x } “ ' (in. 5‘ w} .v {:43 ’3; MA Wiv— 33 Me 2.3: 5 [5 pts each]. At which points are each of the following functions continuous? x+1 a = ———————— () y x2+x—2 Page 4 2008—9-12 »~ \ x" v f \ “‘7‘ 7‘ a? X», i .3. . . - w... M ,, \ : “"3? 1?“ W a x . m ., sm 5' >9 a _ A 4" X “F « {'1 x 1 if“ a r "T" g a] , “R f E 2‘ Q ‘ “me Q; “2i :_ T; 5? i’ " a a ‘.€/f/€Zfir’\, f; 1%” m u?» M " . 2 _‘ 6 [10 pts]. Use the Sandwich Theorem to find limflngx—gl X—)w x _ ‘ ‘ “X m} {>53 .3 *“s a“? j ‘3 A; ~ ~’ A i “a h s . A « 47° «evvwiwg m; Eff {3“ y J y w“ '3 y ‘ 1 4m 1 3? _ ,-’\ w (“V f“, A?» w “‘1 A; " ' {pinata}; emf: I); j 3 V3“: \w’ i” m“ r“ f 7 m «Kym f} “ 2% gr " ml 2‘: “:3 "a (D f a q :31 . w, 5 f M; {5‘1} ,5 y ,5 w {J W Egg? "7? iii/ah .wwwmanJWM’Lflmw,” WM (“mvmummfl M. g; {55 a,” ‘2 K. ’ 4 W mi ‘““'N {mm-v; 3 ‘ $1.3 m i» ' ‘ é" ” “j 5d; «fig/wigs; 5:“ ...
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Test1-Sol - Page 1 2008—9—12 Name (Print...

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