Limit along a path help

Question

Limit at a point along a path

for each k in R find the limit

(x,y)-->(0,0) ((x^4)(y^3))/(x^10 + y^5) along the path y=kx^2

I have plugged in y=kx^2 and i have k^3/(1 + k^5) from here I don't know which of the following answers is correct and WHY.

 My answer options are: (A). [k^3/(1+k^5) if k ≠ -1, DNE if k = -1] (B). [k^3/(1+k^5) if k ≠ 0, DNE if k=0] (C) [0 if k≠-1, DNE if k =-1] (D). [0 for all k in R] (E). [infinity for all k in R] which one would it be? plugging in -1 for k gives undefined which would mean it DNE right? so would it be (A) ?

Answer 1

right that A is answer

for all x except x=0, but including x->0 f(x,kx²)=k³/(1+k⁵)

if k=-1 then the expression is -1/0 which does not exist.