MATH 102 Midterm, Summer 2013

Name: American University of Beirut Time 60 minutes Math 102 Quiz I (Summer 2013) ID#: Page Grade 2 /20 Total /100 1- Let f(x)=Vx-7. a. Finda formula for /7'(x). pmo . Z 3 pts) Ye ¥x-7 — ye x-% X= Yt The amuecse function in fa 47 fity= x 4F b. Determine the domain and range of f and f - Doman if f= is tuo) = dene of £ - ~/ 3 pts) Route of # = [0, +) ca lima of 7 2- Find the following limits lim e~* In(x? +4) = a be beet) [2] xa” x 7 A pts) 2 OK € er H.R. = © = tw ol) x x —— ex(x+#) * 5 (5 pts) e tim (¢ 3) 4c) (o2 ( i) L Llee x) oe x20 21 ° _ a elim sa o Aur se = (5pts) x— 0 In(sinx) L& meet, 4. Find the derivative & : dx © y=3 +tan'(2x+7)+In2 yie 37% Ms 6 + —#* +0 J i+ Qty)* pts) (5 pts) ° y=cos' [In(3x + 5) i a, he : z ee BRES Vy i- faxes) J t= faBresy) e y=(sinx)* (6 pts) buf 2 Ane (ainsy™ ti Any = cox tc lanx) yf! aring ta een) + Oe TOT “YT a _ Cex dé. Le nx Ay | Avex - ax Anne 4! = ( Ann % ) + ox) G ‘) 5. Simplify the following expressions os g 4 4 <5 (3 pts) 2 efln3-3in4 oe ~ tu # - 2 43 3 (5 pts) e log, |inV7+e +7 }+ in\7+e - v7} Acq, | 4 (V7 ria) (yar -)] _ | + (fre Al = 49, (t.2) = top 3=4 3 “a 3 6. Evaluate the following integral , tnt tat . fro ae - a f° . i a2 ? =x tl he : br i 2. ts) ote . 5? e's, wil, pts) ° ie dx Art -4i su —_ “eS x = 2x rly 2 dee nl u ack = tide th 5 du > 1 rs ee ae x? 2 2 Ms “Vy - £ #4 & * dnb ] P on’ e [oos? x sin? x dx _ fe hun % cov ay pts) _ 3 ¢ = ur uh 4 = Ait _ Ah” 4 C_. 2 co 2 4 © foos3x sinSx de = fn tn 3% Ay ) pts) pts) _ »., Be - 2 - OSx) cos + as)enm yacoy § SOE Ne 2 4 4 7S he 2 a —- Sine ae if con 2 Oo 7 fx? nx de pI Any | Xd dd, "2 x 3 = 3 - Oa -L [Rdee Phy -t EEC “a 3 3 S i 2x41 | dye! Aye x? —7x+12 (x-2) (e-#) 2Qnt! ~ A 42 a, x-3 x4 pts) yi Ay +5 [yy +4)+ | yrr) +l lot gi rzeu , tye 2 | Ae a tesla C + l Han les) 4 C_ Se pe pts) 25-4x? Ax = 9 Ane ea’ 49 geo _ . Lz L 52 Ax)” 7 nal - By Amt 2 Cha ce le - (2). 1 | 4me cob Ado pa “CZ -_ /25_asswe /i-sine _ 5)”. 2 Au tne de = (2) it hl PF rip i? £ jeoe| 2 wot . ae et de = (Ds “et fb s Leino-en® } 2x : =e. | > - (2) | [ -— web] +C V2s—4x* Q/ 10 2 6