# How do you find the limit of the piecewise function f(x)={(x^2,if x text{ is rational}),(0,if xtext{ is irrational}):} as x approaches 0?

Since ${\lim}_{x \to 0} {x}^{2} = {\left(0\right)}^{2} = 0$ and ${\lim}_{x \to 0} 0 = 0$,
it is safe to say that ${\lim}_{x \to 0} f \left(x\right) = 0$.