Question

3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.

Answer 1

③ cal fogy) = xtxtyxy - x-y How , lim fogy can be wridden as (Any) 7 Corol an curre a y=ho fas sone n. lim tathmat Но — — lin x63 HP RX²) Х-д и i-h) lim x² HR-1293 Bose im htm mo Hence, lim fanya (exists) any Hono cxtyt ab (44) +1000) fony) = 4y - a o el (x+4)=(890) Now, on curre y me Hlim fonn lim xt pt.at 044) 8690) to the lim xe pt. x ² =o=ffono) to tra i fory) is continuous at cogo).

1 al 3x25x4ftanny=0 Differentiating w.rot. ex. we get .6205(+xdy 7+ Seezy dom =o 61–54-5o da secoly) (y tady los & secay) -5x dy = 54-6X-4 second dy - 54-62-y sexy) - seczory)-571 (A) xlny + sin Oly) - t Let, FOGY) - play 4 SH (2-4) - T Have isng Implicit differationis , we get - - Fx I thy f GS (A-47 +68624) 602 g(lnytas (29) Hos (24) =