Let f(x,y)={((xy)/(x^2+y^2)",",(x,y)ne(0...

Let `f(x,y)={((xy)/(x^2+y^2)",",(x,y)ne(0,0)),("0 ,",(x,y)=(0,0)):}`

A

f Is continuous at (0,0) and tha partial derivatives `f_x,f_y`exists at every point of

B

f Is discontinuous at (0,0) and `f_x,f_y` does not exists at every point of Rs

C

f Is discontinuous at (0,0) and `f_x,f_y` exists at only at (0,0)

D

None of the above

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

cos ec^(2)alpha=(4xy)/((x+y)^(2))[(x,y)!=(0,0)] is

Let f((x+y)/(2))=(f(x)+f(y))/(2),x,y in R, if f'(0)=-1, then f'((x)/(2))=

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

(xy)/(x-y)=(1)/(2);(xy)/(x+y)=(1)/(5) wherex +y!=0;x-y!=0

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f(x)-f(y) is equal to

Solve the following pair of equations: (2xy)/(x+ y)= (3)/(2), (xy)/(2x- y)= (-3)/(10), x+y ne 0, 2x-y ne 0