Exam1Solutions - MATH 150 Midterm Exam#1 Dr Sam Shen Spring...

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Unformatted text preview: MATH 150 Midterm Exam #1 Dr. Sam Shen, Spring 2008 Student Name Student ID Studeni Grade I100 1. [E0 pointsl (3) Find the composite function f o g if fix) 3 x , g(x) =sinx 1+x Risky M ,1" , 5,; , ‘. M iii/”$53? " "i" agrw-L} ~~ g—a: 3: w‘)! (b) Identify the domains of f(x) and g(x). ’1 Efiw‘ial'Wg “if: $96,-i) Lit-3,93} 5""; 2. [lfi points] Find the exact value of each expression. 7-! (a) 10g5125 3; A C)“ v ...¢ :23 KP—‘N (Elk—- \_~__/ arctan 1 ,z (C) W i”? ; arcsin[y ) ‘5 Li Lia W TVQ. 4“" , “3/5? Page 1 of4 3. {25 points] Evaluate each of the following limits if it exits. (a) limw ,rwai ' «L “we“ #4. H f! U E 7:? £25??? 35% a" 4 5‘ ~ ix --%- 5 ~ >5. 4 x .4 g.- s , "" ’" ‘ _,,_,.,..,...u 4 , MMW‘ , 1,4 r? 5 4.. rig; 4 4 __.-—- ' 4a.! :4: 31 r; ,3 4, a" , 4 , *2- z; .4, a 3 . ‘ - , em. ‘ $44 3 {5‘ 3*” 'W ‘3" 4- J A a,» , 4 4,4. g «1 if?" 4.4. - 4 4 44 ,, 4 4,! h ¢ um}? a, .79“ 7-“ r f (6) lim arctarifl x l) xwa—m Page 2 of4 4. {10 points] If 2x 3 g(x) _<. x4 —- x2 + 2 for ali x, evaiuate the following limit iim g(x). Cite an appropriate theorem. x41 cx2+2x x<1 5. {10 points} If fix) 2 , x3 —cx x 21 find the vaiue ofc such thatflx) is continuous at x=1. '2 g ,m E: = Avg “p, . w" I“ ‘ V, ’35.. aw a a ‘49 "z :‘ fv r «C ‘: - ' 4” W4 (5.. g f a“ I Ft“! 3’3 ‘ n r} (:4; A: 3‘ z. i: L - 9’2”; r": 15.4 u, (a g i a ” r» 231: :32 ' ' We 6. [15 points] Solve the equation lnx + En(x — 1) = 0 for x . _{_. fag»? w, ‘3 «if; 3; 35 :7; .._. {,3 s"; ‘3!” If g u} " i r l _' r' v f; n X ., q {3 a?» W i “7 ”h «.2. J .2; 2.1 Page 3 of 4 7. 110 points} Prove that the equation 4x3 — 6x2 + 3x = 2 has as least one soiution in the interval (1, 2). Cite an appropriate theorem in the proof. ”7 a. ’5': .w t" - . J ., s" €5,155}; Jag-33$ ”€3,155 8. [5 points] Find a formuia for the inverse function of the foilowing function I X = . f() 1+2x >( g f Kg; 1; g X y £3 J; g {ii-éix) « X $75 2% 9; 3: a}: 5,?ny >v 5 "g {3; szga»%} 3 “§ W WV: 5- ”g r ““6wa EEJJ. ml A? J54. éem-é: JJJ Page 4 of4 tit"; ...
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