qestion 1

If fsubx(xsub0, ysub0) and fy(xsub0, ysub0) both exist, then f is continuous at (xsub0, ysub0). Prove or disprove

Hint consider the function defined by f(x,y) = (xy)/(x^2+y^2) , if (x,y) is not equal (0,0) or f(x,y) =0.

question 2

Let f(x,y) = (sin^2 (x-y))/ (abs(x) +abs(y) ).

Prove that lim as (x,y) approach (0,0) of f(x,y)=0.

Hint: for all real numbers m and n. abs(sin(m+n)) smaller than or equal to abo(m+n) smaller than or equal to abs(m) +abs(n).

note: abs(m) means absolution value of m.

Thank you very much