Prove that the function `f(x)={x/(|x|+2x^2),x!=0 and k ,x=0` remains discontinuous at `x=0`, regardless the choice of `k`

Prove that the function f(x)={(x)/(|x|+2x^(2)),quad x!=0k,quad x=0 remains discontinuous at x=0, regardless the choice of k.

Prove that the function f(x)={x/(|x|+2x^2),\ \ \ x!=0k ,\ \ \ x=0 remains discontinuous at x=0 , regardless the choice of k .

Prove that the function f defined by f(x)(x)/(|x|+2x^(2)),x!=0 and k,x=0 remains discontinous at x=0, regardless the value of k.

Prove that the function f defined by f(x) = {((x)/(|x|+ 2x^(2))",","if" x ne 0),(k,"if" x = 0):} remains discontinuous at x=0, regardless the choice of k

The function f(x)={[(|x|)/(x) , if x!=0],[0, if x=0 is discontinuous at

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.

Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if x ne 0),(k, if x = 0):} remains discontinuous at x = 0 , regardings the choice iof k.