Mathematics I for IMD

tffi Carleton UZ UNIVERSITY Final/Deferred EXAMINATION January 2005 DURATION:3 HOURS Dcpartmerr: Narne & Course Number: BIT 1100A CoLrrse Inslructor. Jtaltang L Students MUST count the numberof pagesin this examination question Paper beforebeginning to rnrrile. and reportany discrepancy to a proctor. This question paperhas 2 pages. No.of Students: 1 This examination question papershould be takenfrom the examination room. In addition to this question paper, students require: an examination booklet a Scantron sheet l. Evaluate the follorving limits (4 marks each) sin 3.r b. lim,-o i[+8-2 -1\ I yes no lirn a. -v I r- r I c. lim . ''. -' ,_,_ .r, _4 I rlr 3x-+3.r+l' ti. rrl-rr. _ -----:---------- '-* 2x' + 2x-+ | 2. Find the derivatives for the given functions. If possible, simplify your answers. (3 marks each) I a. c. '-l . sln ,r I ('\,1 = ---. sln -\ l'(r)=ln(sinj-r) ,f (-r) = 2' arcsrn(x') * ,' 3-4sinx i. I t-r.t = -------------7 ' 3+4tanr/x b. d. .f (x) = "f (x) = e. (2x + l)2 e -f e I BIT I1OOA DEFERRED EXAM - FEBRUARY 2OO5 J. Sketch the graph of / t r ) = ,ll , makinguseof any suitable information you can get _t -l fronr the f'unction. e.g. its first and second derivatives, asynrptotes, etc. rl-l nrarks) l. Evaluate the givendefinite and indefinite integrals nrarks each) c f---l a. J r/.r'r/-r b. Jcost xsin r xrlx r I cos{r c. | ---- t--d.Y J | .- r. 1-\ L-) 6 | ', I , e. | (.\ -r .r )(/.\ -.1 3" --t f' l-l--i-dr '"x-+9 bounded by the curvesx = y2 (4 n t d. | ,r sln .rd_r 0 ]tt 5. Find the areaof the region \-axis. 6. Deternrine ll'hether the given those l'alues. Also discuss the a. l'(-r) = .rr + I on [0, 3] 7. Find the inverse of'thefunction v = 8. Evaluate the following. ^logl(-) -J' ,, 5n. t;ilr (turt(-)) 4 functionshave any absolute extreme concavity of the functions. and x-l=2 andabovethe (8 marks) values, and find (4 marks each) e' b. f (*)= * on [2, 3] a -t,J,. cos(sln'(-)) ' .4" ,slnsinr +(lnetot.')r l.-e' (4 marks ) (5 markseach) a. c. b. d.

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