R= Reals
Let f, g be defined on A as a subset of R to R, and let c be a cluster point of A. Suppose that f is bounded on a neighborhood of c and that the limit as
x --> c g=0. Prove that the limit as x --> c fg=0
R= Reals
Let f, g be defined on A as a subset of R to R, and let c be a cluster point of A. Suppose that f is bounded on a neighborhood of c and that the limit as
x --> c g=0. Prove that the limit as x --> c fg=0
If $\displaystyle f$ is bounded on a neighborhood of $\displaystyle c$, then $\displaystyle -M\leq f(x)\leq M$ for some $\displaystyle M\in\mathbb{R}$. So $\displaystyle \lim_{x\to c}-Mg(x)\leq \lim_{x\to c}f(x)g(x)\leq \lim_{x\to c}Mg(x)$
Proceed using properties of limits.