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?

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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#.