A function f(x)f(x)f(x) is continuous at x=ax=ax=a if:
f(a)f(a)f(a) exists
limx→af(x)\lim_{x \to a} f(x)limx→af(x) exists
limx→af(x)=f(a)\lim_{x \to a} f(x) = f(a)limx→af(x)=f(a)
The derivative exists