Question

Let f be the function defined below on the given region R, and let P be the partition P = P x P. Find L(P). f (x, y) = 2x – 2y R:03 51, 0 Sy 31 1 P = - [#. - ( a) OL(P) = b) OL(P) = 1 -0) OL(P) = 1 1 1 1) O L;(P) = 12 ) OL(P) 7 12 None of these.

Answer 1

= 2x -29 f(x, y) R: = E (X, Y) 105*51, 08431} PL = Pos 1,2,3,4], P = [0, 5, , 2] The partition is has five points implies that n2 =4 and for P2, n₂ = 3 Then, 1 n = n₂ X ₂ = 3 x 4 = 12 - Note that for the lower Riemann sum f(x, y) = Min (, YER;' = [X:-1, 3;] * [i-2.4;] f(x, y) = f(0, 0) f(x*,y) =111,0) = 1-2 texty = f(20) fle, o). taxes, y ) = 110,) = .-23 f(x, y) = $(, ) - 4 -- f(, 4.7") = +(3, ) = 1-33 - fr xot, 4, ) = $ Fla) -1 = . 2 f(x,y -116 wilt

ง | F(x,y) = f (0) = (x , ) = f() = - = (*1, 9.1) = F(를) = 4- - - f(x, ) = () = 롤 - - 농 A Ay A1 = AX, Aya = ()() = 뉴 A = AX2 일 () 에 DAI As = NX, As = ) () = 1 FI A12 (PF) - MA2 * z f(x,y*) AAL [ f(x, 4SAA + + + - - ] 변 J2. - 나P | 2 11 12