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?

Question

6738 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-28T22:02:03

Since $lim_{x to 0}x^2=(0)^2=0$ and $lim_{x to 0}0=0$ ,
it is safe to say that $lim_{x to 0}f(x)=0$ .

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