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 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 \(\displaystyle \lim_{x→0}x^2\cos(2πx)=0\).
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 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 \(\displaystyle \lim_{x→0}x^2\cos(2πx)=0\).
