{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1802A-IAP_Exam2-Solutions-2010

# 1802A-IAP_Exam2-Solutions-2010 - Somme/J.527 NAME email Rec...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Somme/J .527 NAME email Rec. Instructor Rec. Hour 18.02A Exam 2 — IAP 2010 Friday Jan.19, 12:05qlpm Directions: There are 6 pages, printed on one side. Answer all questions, using reverse side as needed. No books, calculators or notes. Fill out the above line, then proceed with the exam. Problem 1. (15 pts: 7+8) Consider the vector ﬁeld F = 33} i— a: j. Let C be the curve y = 2:3 from (1, 1) to (2, 8). 2:) Compute the work done by F on a particle that moves along 0. 117‘ M: 3/ , /'/ = — x PkVp‘k‘c/g’rt—LLC C 'I )K .2" f r 7": ((3! .1 E74 57,2 ‘c “k K‘ l "l\ W "l K "7x I B K m I I O b) Compute the flux of F across 0. ”Erin sage v-c makefhi-guﬁm‘.‘ J ﬂ 7 3/5 74/” /\E #5 -: /‘~—/Vp/x r/ol/{f :. ~/l/d+ C . I 3‘) Problem 2. (15 pts: 5+5+5) a) Find the‘value of a for which F = (2323,12 + 22:) i + ((22:23; — 23;) j is conservative. '--‘—‘V__'——- m b) Using the value of as found in part (a), ﬁnd a. potential function for F by any means. F = 17/ Jinnah w m» = xzywn w _ 1 z ”Z 4 ‘2)(‘7-27 ‘5" 7““7) - V 7 ““7 + ‘16" c) Find f F - dr for the a—vaJue found in part (a), where C is the curve: C a: = 3 003225, y =sin2t, 0 S t 3 7r. r“ .—J 7Z‘__iey— 1': Vf _ A g —> v.54. “all. ﬁns. a/Ié/EVL/HJ 1" : f/é'vlﬂwli‘) *fﬂv‘m‘ ﬁg") = /@,0}—//320/ T- O - .._ ._ _ _ O Juncc, gas/1) POI/VI -" f“?! X 3‘ 7 JTrﬂféT?U/NT " (4:0. X=P-7:O Problem 3. (20pts: 10 + 10) Consider the vector ﬁeld F = 2:33; i + (y — yz) j . a) Show that the ﬂux of F across any simple closed curve C is equal to the area bound by C. b) Use part (a) to evaluate the ﬂux of F across the curve 0 consisting of the semicircular are on the left-hand side (:1: g 1) (if the circle of unit radius centered on (:c, y) = (1, 1), being traverse from (1,0) to (1,2). Hint: ﬁrst draw the curve C. C/DSI— C ut'ﬂ 1‘4e Sﬁnsz-f- i/qu't (I 724.. itébvc refute/7" Ih/(v'é-qécf / a - 77‘ ': —' - f " ’— C+Ct ‘2 / / 2 J‘u‘nrt: E Mum-Ia! / ‘ T ‘g dooéA/ISf. .; ”' A _-,_L (1". F- 2 if 7" F M [5. E Z e W «7/7" as:— r» ”We /V°w 0H (J , le I II): 1 0 I JD 0 a 0 I. _, _ 2 ,c = - ~7 /P;~,,U=//M,t7_/u/M — 77 7 L 2 _ c.r C, . Problem 4. (20pts: 5 + 15) a) Sketch the region R contained within the pair of lines y/ac = 1 and y/a: = 2, and the pair of curves my = 1 and my = 2. b) By making an appropriate change of variables, calculate the area of the region R. 4+ M‘vxy , V": y/x ....r :- (){L{, V/ “- J 3/107) _ 3‘ S H \ “'1 Problem 5. (20pts: 5 + 15) 3.) Sketch the domain D contained between the cone 2 = (a:2 + y2)1/ 2 and the paraboloid z = (2:2 + 312) /a. Calculate the curve of intersection of these two surfaces. b) Compute the volume of the domain I). 22;» 1/ T== // w=-///z e M .0 4e 9:; 277- V226! 83a. Problem 6. (lOpts) Show that for any continuously diﬂerentiable scalar functions f(:£ y) and g(:1:, y): fwwnzgigm , where R is the region in the asy— plane bound by C 6.15.13'ﬂn1 : //’§ t/CW/ /' #4 C. 3//” Vj at; // :r/K/Vj) A A; ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

1802A-IAP_Exam2-Solutions-2010 - Somme/J.527 NAME email Rec...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online