MATH 201 Exam 2, Fall 2017

MATH 201: Calculus and Analytic Geometry III Fall 2017-2018, Exam 2, Duration: 60 min. | Problem | da 1b | Ie | 2 13 4a 4b | 5a | 5b Total a _ 4 i ae 2 i ll. -. | | | Ponts 7 7 7 10 | 20 10 | 10 | at Sp + | eet Scores | | 7 Za | | i ) } CU bs | — | Snr ee A ce © | [=u Name: AUB ID:|_< Please circle your section: Section | Section 2 Section 3 MWEFE 3, Karam MWE 3, Karam MWFE 3, Karam MWE 3, Karam Recitation F. 11 Recitation F. 8 Recitation F. 10 Recitation F. 9 Section 5 Section 6 Section 7 Section 8 MWE 10, Shayya MWEF 10, Shayya MWEF 10, Shayya MWF 10, Shayya Recitation T. 11 Recitation T. 12:30 Recitation T. 2 Recitation T. 5 Section 9 Section 10 MWEF 11, Yamani MWF 11, Yamani Notes before solving the exam: Reakition P 3 Neciaiion F. ¢ 1) You have to solve the recommended Section 12 Section 13 problems in the book after understand- MWF 2, Nahlus MWE 2, Nahlus . Recitation M. 8 Recitation M. 9 ing each chapter from the book and the a notes. Section 16 Section 17 ; ; MWE 9, Mourtada \ MWE 9, Mourtada 2) Please understand that this exam is Recitation Th. 9:30 / Recitation Th. 2 solved by students, and it may contain Section 19 Section 20 some mistakes. MWE 1, Nahlus MWF 1, Nahlus 3) If you have any questions or con- Recitation F. 10 Recitation F. 8 cerns, let us know through our mail: in- Section 22 Section 23 sightclub@gmail.com. MWE 10, Abi-Khuzam MWF 10, Abi-Khuzam GOOD LUCK:) 1 Recitation F. 4 Recitation F. 2 , Section 26 Section 27 Section 28 MWFE 11, Aoun MWE 11, Aoun MWF 11, Aoun Recitation Th. 11 Recitation Th. 12:30 Recitation Th. 5 INSTRUCTIONS: (a) Explain your answers precisely and clearly to ensure full credit. (b) Closed book. No notes. No calculators. No cellphones. (c) UNLESS CLEARLY SPECIFIED OTHERWISE, THE BACKSIDE OF THE PAGES WILL NOT BE GRADED, Problem 1 (7 pts each) Determine if the limit of each of the following functions exists as (x, y) > (0,0). Explain ie 4 bat im yt gQ Kher by CIT ~>0 2 ee (b) g(x,y)=— |x/+9y4 | \ x\ a hut Ain | _— iv\= im wy) >e = \x\ ney 7 (c) A(x, y) = —2 INSIGNE 3y —4x el i *(4 ox 3 oe ED, A sight Si NCE the Lmb is in tums f my thon if the Prmck hes Veen G Vales hu | Fferen Vales fa SS fim dgesach exy + insight c ku (10 pts) Consider the function (x, an Problem 2 Find the domain of the function f. Decide shea ae aoe of f is an open region, a closed region, or neither. Also decide if Domain f is bounded or unbounded. Problem 3 Check beck Fg t { | (20 pts) Find the tangent plane and normal line to surface 2x” +40” =6-3lnz at the point (1,0,1). 5 ~ Problem 4 Let f(x,y,z)be a differentiable function of three variables. Suppose that Vf(LL2)=6i-2j+k Vf(6,2,.4)=i+j+k Let % r +2s —_— z=2r+ins _ “ 7 : - : 7 | ie ow Ow (a) (10 pts) Find oe 2, at the point (r,s) =( or s ala Thefalowing seat. I pack EY are Bias q ae wk for (rs)= Cor) Priests lw dw dx a... db ol ~~.) —- oe . BOY vo ige or gx or ws oy Ar Az Wen Insight = Se es ary ‘ Fe 9s | BIGRE e ku 6 (b) (10 pts) Find the minimum vata and imum value of the directional derivative of S (x,y,z) at the point (11,2) (Daf CS PIN MUN when cos (@) -s Im @ (tr) = ~| Hn fy py whch. ker =) Problem 5 (a) (10 pts) Find the Taylor poly: x) generated by the function f(x)=A/1+ x at the center a=0.] 7