Chapter 13.2, Problem 30ES

Determine whether the statement is true or false. Explain your answer.

If $f\left(x,y\right)\to L\text{as}\left(x,y\right)$ approaches $\left(0,0\right)$ along the x-axis, and if $f\left(x,y\right)\to L\text{as}\left(x,y\right)$ approaches $\left(0,0\right)$ along the y-axis, then ${\lim }_{\left(x,y\right)\to \left(0,0\right)}f\left(x,y\right)=L.$