Limits Across Paths

A limit ${\lim }_{x\to c}f(x)$ along path $c_1(t)$ is equivalent to ${\lim }_{n\to c}f(c_1(t))$

Example

Consider limit ${\lim }_{(x,y)\to (0,0)}\frac{x{y}^2}{x^3+y^3}$ along paths $c_1(t)=(0,t)$ This will be $f(c_1(t))=f(t,0)=\frac{t^2\ast 0}{t^3+0}=0$