2nd Midterm Exam

# 2nd Midterm Exam - £2[WT—H 20"3 W Q1(10 points...

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Unformatted text preview: £2 [WT—H 20 "3 W Q1. (10 points) Determine the critical points of the function f(x,y) = 1 -— 2xy -— x2 classify them. — 213:4 and for points on the plate deﬁned by x2 + y2 < temperatures on the plate. [m‘rcrio‘r1 '2‘ 7‘ 2(7-k‘j) :3 f (9 :. LLyx+ﬁ) 2.073% :"X % \\ gﬁhce a 51 Q “I a my“ """""" "f X/ ’3") 9 Qua-x." i 2. L g. 9 { —-' -~ 0 1 “ (Hmm) .: My, —F5 xé; (\$1: (I) a -. “z. 1’ 1+ ‘7'! h? '5‘ .F m1(x+ 2: x iffy-xiv) (:,:) 90 9V1? dam ?( g: 1 5' :3 ( 51(9)»!(“53 9) ““ ~mwm." m3; __ - , ~35 x +.§2§-x1 1w: *T-ug ‘35 K?” : zeta-(2 :55 27(2- 1': 2.5- ”“ B W ‘7 . .r ‘3‘) Ox 2—1 i" 3... :"x '3: ~K- a”... 13.2)) T j; .7 J \ﬁl‘wf?{ .— \R \‘3 ‘13,, \§‘"m1 3) *5" - ..._ X z: I” ‘" \f‘ 7‘ 2»- =~> ! '2: .9 M\ \A at) b) Q3. (12 points) Let R be the region bounded by the line y (3) Sketch the region R. = x — 1 and the parabola y2 = 2x + 6. (b) Set up the double integral ffR f (x, y)dA in both orders dxdy and dydx. z (c) Find the area of the region R. ?. __ —— 5' “.29 (x_t3=zx+{ =5 7‘ WC FAsteLt—XM 9H ~_ (Qt/-23 My)” H a“ gram rs] ft ﬁxogﬂ ’2. -2 1:2 '2. ~\. “"‘36 _3 -m K ' m +§D g gamaﬂ Q —1 x—\ '4 am H: I '2. u 1 2. lj (bydv ii?) 0” :' :2: -—>. 3 _-; (3+\€'%)’(2’g+?) :3o—\1 3‘53» =3 (x+!)(X—F):° . ” ” sin y (14.00 pomts) Consider the integral I I dy dx. 0 x y 3) Sketch the region of integration. b) Reverse the order of integration and evaluate the integral. A) :x wee-Li" %/ {my 699‘31‘1- o O : f” 5M “Adam 3 ‘3 __ ix. :— "’ mus] 2., 2 31 9‘3 1 1A .E H: X14133" “'4'?- L 1x1+13 1 14—an gﬁ f 1—992- Vﬁr #94 g <9 (Mara/93 0 1“ _ Z _ 2_ 2 Q7. (10 points) Evaluate the integral f: f_}1—_{x—2fx22+:z y (x2 + y2)3/2dzdydx, by changing to cylindricai coordinates. W1 9 3W1, : [2 L W1 5” ) (3.5:: -— E.) ...
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2nd Midterm Exam - £2[WT—H 20"3 W Q1(10 points...

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