101-2007&2008-3-M10-July2008

101-2007&2008-3-M10-July2008 - Kuwait University...

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Unformatted text preview: Kuwait University, Department of Mathematics and Computer Science Calculus I (Math-101), First MidTerm SUMMER SEMESTER 2008 JULY 5, 2008 DURATION : 90 MIN Calculators, Mofiiles and Pagers are not allowed during exams Question 1 : [2+2pts] Find the following limits, if exist 62 [5) lim 3: + 25in{$) 1' ___.. (a) 1m r—éfl tan(3:t) — I (9—1-0 1 ‘ 2+ a C05 (9) Question 2 :[5pts] Let in; — li(z — 2) “3): (mg—33+?){xr—4l Find all points of discontinuity off and classify each discontinuity as jump, infinite or removable. Question 3 : [413115] Let _ 35::2 + r]:r| flea: HI) Find the vertical and horizontal asymptotes for the graph of f, if any. Question 4 : [1+3pts] (a) S-tate----the Intermediate Value Theorem. (b) Given two continuous functions f and g on {—00, 00) such that f(0) = 9(1) 2 0 and f(1) 1 9(0) = 1. Show that, there exists c E (0,1) such that f(c) = 10 9(a). Ci Question 5 :[4pts] Find d—y, where I 51 2 . 3 y = sec(1:) tan(3:) + I Question 6 :[4pts] Find an equation of the tangent line to the curve Wm atz=1. y=fi+1 TERM; ‘5 , m8 OMAN T Vim-k Nuclkfm \ \.C\\ Sma; _,\L_._.__G;5‘l _L_\ __. \_§___¢.\ —— 1 Q (9‘ _._> 3 l-ncGSQlQ} '9 (9/3 é _g._ $- 4911 V9.1 yuan}; Vacuum] macaw/‘7 a+cosuwi 54% Urn .91‘ z: o . 9—3.9 1+GSC‘le S: X E) Um ___q__x+a.‘$mx_ : LA —.__._\-+1 a 2 1. fi—Fvo Erma-n -—>< x—evo M190 '2 '5 —\ "5x ‘1. E93; not CaJrznoous oJr ~><:.\ ) 7&2")— cxmok x:L+. Um \vt-H {xx—LN _ i l. a? 31% (”Jr X-\ x_,.\'-"+- Ex—\\£X‘11Lx_ua - 1" A um \x—u (x —2—\ .. .__\_ :7 PA). odr 7‘31 when. (”X-\th—LfiLX—LP} " ‘9— — um \x—u Cx—‘t-‘N _. __ 3 __ “Kn—39L»: Cx—l‘xLK—‘DCX~LH ‘ +00 #7 I'F‘b' Y‘““*' 3. v-m: —><=o um M : O :> No \LCA. Kai) xR’x—uj x:\ Um,———————-—3x1+1vxl '33-’00 “—2? x:\ MON'R' x—pri‘ ’7CC")€-—\\ MIA: um —___."57‘L* “‘9',“ : 1 43.) ‘A—z’z. {Am \—\.(A UM 3961+9C—‘96\ _ __ .- - CM \J‘_Q. x4506 art—x -' L+ "9 5"“ M 1+. m vac Run : ‘Ecm_ko°5cfl. Rem in Mcnmus cm Eon—J.J Kan : -m 40 and RC1] —_- \ so , 0 mm more) (2/9120) :2) ($3 'LxLT ‘3 C e {ugh at, Rcmro 2) fl'cfi'TTO'Qfi‘c). QLE, ‘L 5- : S—CJLI’K To. LL x + «\x WK _ “—1358. €_ Qt Xr't \j : O ‘ I ‘ -—--— 3‘ .__ £57: +0.. xii —K&_>'<—\\- mt; : t KR+\T'- Gkfi+\\1 a m = ‘a . Weteg—WE) om equuhmfi an“? QM {s \i: fix —--\-— . O. .9 q ...
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