1 1 l l j i o fi 1 1 1 1 1 f d 2 1 jl 71 1 l 32b

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, '1"- '( / ) '1. -+- L( (..l J (I o -, ) ( fI \? , (} -'·-""1 1'~~ .-'-_. -1 ~ 1 ,_. .~ + 1 f~ D 2 .., 1. Jl 7/1 , '1 L
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32B MIDTERM 1 RADKO Problem 3. Compute the area of the region in the first and fourth quadrants outside of the 4 2 curve r = .j2 and inside of the curve r = 4 c (). ~::( ( if,) -~ 2) J {i .0 J"'~' (,\ 1{ )~' ">: ~ .--:=~ j I [ V .> i / I ( '1 I -) ov-" l~ ~
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5 32B MIDTERM 1 Radko Prohlem Sketc .. llie region of integration and compute the integral: ... -._--- If(JL.1' ~ 2 2dydx. vi x + y ,.,-- ( / 7 ( .11-)l J (I-; / )J J j ! ./'2.. V "1. t Y r rv'9=XI Jo Jo if 1. /'1 .. :1 Y "-Ie I J \ _.- )
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6 32B MIDTERM 1 RADKO Problem 5. Multiple-choice questions (scoring: 2 for correct answer; 0 for a wrong answer): (1) Let f(x, y) = e Y + y2 . Let V be the volume of the solid that lies under the graph of f(x, y) and above the rectangle [0,1] x [0,1]. Divide the interval corresponding to x into 3 equal intervals, and the interval corresponding to y into 4 equal intervals. Let Land R be the values of the Riemann sum computed using lower left corners and lower right corners respectively. What relations among V, Land R are satisfied? ~L<V<R; . (b) V < L, V < R; (c) V> L, V > R; (d) L = R; V > R; (2) Which of the following is NOT true (here J denotes the average value J of a function f(x, y) ~ 0 on the region R): (a) The volume of
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