102-2006&2007-2-M10-March2007_2

102-2006&2007-2-M10-March2007_2 - Kuwait University...

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Unformatted text preview: \. Kuwait University Department of Mathematics and Computer Science Math. 102, Calculus II Date: 24/03/2007 First Exam. Duration: 90 min. mm Answer all questions. Calculators and Mobile Phones are not allowed. 1. ( 1+ 2+3) pts.) Let f(x) = tan—1(1n m) + b) Show that f has an inverse function. ( (a) What is the domain of fins) ? ( (c) Find f‘1(x) and its domain. 2. (2 pts.) Calculate sing +sec‘l(2)). m 3- ((3 + 2) pts.) a) Find 5% y : (sing 005111: + Treat—13 +err. dn: (b) Use implicit differentiation to find g5 if tan—1(3)) 2 In [1 + 4. (3 pts.) Prove the‘following e h(ln ) + csch(l :c) 433 s = . C x “n 3:4 — 1 5. (3 pts each.) Evaluate the following integrals ( ) f 1 dz: ' a a y ‘ xv 934 — 16 1 (b) / “- (c) f—flfl— dm. cos(3:) + sin(a:) OO 99 £01) ;_&csj(pwi)rr7rfi 36::f1: -eaL 777(400 i> o<x<°flzg . _\ R Li Z mltfiwfl)_’ IT/z, : *R/{fk/K'ZTZO J Ziggy L‘Zflnx)”i.fi 7" [if L om). ‘ L ~ . :__J v, Ihv b) 521) :mla >0 wolamun’f “I #0 Meemsfs c) a — CL:(§V\1)+H7L_ :2 Lar{:ta:‘(fim;[email protected];@;0fl:¥wdg. qu— H\ 4.41%); 3. 9L :C‘F‘M :— 'FCM) :1 e MAS OO 99 ...
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