Question

For \[f(x)=x^2\], what verifies continuity at \[x=0\]?

Options

• \[f(0)=1\] and \[\lim_{x\to0}x^2=0\].

• \[f(0)=0\] and \[\lim_{x\to0}x^2=0\].

• \[f(0)=0\] and \[\lim_{x\to0}x^2=1\].

• \[f(0)\] is not defined.

Answer 1

Substitution gives \[f(0)=0^2=0\]. Also, \[\lim_{x\to0}x^2=0\], so the limit equals the function value.