Answer
$$f(x)= \frac{2}{x^2},\qquad g(x)=\frac{1}{x^2}$$
Work Step by Step
Consider the following functions:$$f(x)= \frac{2}{x^2},\qquad g(x)=\frac{1}{x^2}$$It is clear that$$\lim_{x \to 0}f(x)=\infty \qquad \& \qquad \lim_{x \to 0}g(x)=\infty .$$However, we have$$\lim_{x \to 0}[f(x)-g(x)]=\lim_{x \to 0} \frac{1}{x^2}= \infty \neq 0 .$$
