## Answers

3 But Take f(x,y). x3y -zy gry? 2 Iz G, y) = 32 - 2ably sy => Ixcoy = -2 x²x4² Ixy (0,0) = -1 x²-3xy fy(x,y) zyliyyat => Fy (%,0). a 52 Fayx (0,0)=1. 7 Jay & fyn

a) Take 7(x, y) = (X17) 0,0) otherwise Check Partial derivatives al co,o)- 72(0,0) = Lim JCh,o)-100) if the limit exists h ho zlim h Tycoo) lim 300, le) - 110,0) it.

.
The limeto exists Tim the But lin Fx, y) - lim [Taking y along the x²mge? line ma does not existe ] Taman Hence both partial Derivative, existe but the Jun is not continuous at coo) Hence whatever. Skylese is is false, is saying 0 b) By Clairot's Theoremo It all the partial derivacitives of f(x, you exists and be Jay, Tyne are both continuous then Fay - Tyx, For a smooth Coo) fue" all portial dosuratives of feed exists and continuary hence Ixy 2 lyx

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