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MATH 0240 Midterm: MATH 240 Practice Problems-83

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turquoisegnu128
31 Jan 2019
School
Pitt
Department
Mathematics
Course
MATH 0240
Professor
All

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Practice problems on sections 11. 2, 11. 3: for each of the following limits, evaluate the limit or prove that the limit does not exist. a) lim (x,y) (0,0) x2 3y2 x2+2y2 ; b) lim (x,y) (0,0) x2 3y4. 3x4+y2 : lim(x,y) (0,2) (cid:18) x2 y x2+y2(cid:19) ; e) lim (x,y) (0,0) x2y2 x2+y2 ; f) lim (x,y) (0,0) x2y2 x2+4y2 ; g) lim (x,y) (0,0) x2y2 (x2+y2)2 ; h) (x,y) ( 1,1)(cid:18) e(x lim. Y) sin(x2 y) 1 x4 2x2y+y2 (cid:19) ; i) lim (x,y) (1,3)(cid:16) x2y y xy x y+1(cid:17) 3x+1: f (x, y) = arcsin(cid:16) x2+y y2 3x(cid:17, find 2f. Y x , if f (x, y) = x2y3 sin(2x + 3y): find z.

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