differentiable functions

[artemidjaupi]

Can anyone please help me!I have this question.If the function f(x,y) setisfies this condition |f(x,y)<x^2+y^2 then f(x,y) is differentiable at the origin point O(0,0)

 

[HallsofIvy]

Can anyone please help me!I have this question.If the function f(x,y) setisfies this condition |f(x,y)<x^2+y^2 then f(x,y) is differentiable at the origin point O(0,0)

I don't believe this is true! Are you sure you have written it correctly? It seems to me it should be \(\displaystyle |f(x,y)|\le \sqrt{x^2+ y^2}\).

 

[artemidjaupi]

thats the same thing can you help me solve the example you suggested?thank you

 

[Steven G]

Can anyone please help me!I have this question.If the function f(x,y) setisfies this condition |f(x,y)|<x^2+y^2 then f(x,y) is differentiable at the origin point O(0,0)

Sure we will help. Can you first tell us the definition for f(x,y) to be differentiable at the origin?

 

[artemidjaupi]

the definition for a cunction to be differentiable is lim (x,y)---->(0,0) {f(x0+x,y0,x)-(fx0,y0)-df/dx(xo,yo)x-(df\dy)(x0,y0)y}/sqrt x^2+y^2
but since i dont have the function because it is not diffined |f(x,y)|<= sqrt x^2+y^2 i cant find df/dx and df/dy