1) A function has to be continuous at x=a if the lim exists. 3) If there is a vertical asymptote at x=a for the function f(x), then f is undefined at the p...1) A function has to be continuous at x=a if the \displaystyle \lim_{x→a}f(x) exists. 3) If there is a vertical asymptote at x=a for the function f(x), then f is undefined at the point x=a. 4) If \displaystyle \lim_{x→a}f(x) does not exist, then f is undefined at the point x=a. Since \displaystyle \lim_{x→0}x^2=0=\lim_{x→0}−x^2, it follows that \displaystyle \lim_{x→0}x^2\cos(2πx)=0.
