Suppose I have two continuous functions on $\mathbb R$, $f(x)$ and $g(x)$, such that $f(x)\leq g(x)$ for all $x\in \mathbb R$ and $\lim _{x \to\infty }g(x)=0$. Is the following true: $$ \lim_{x \to\infty} f(x)\leq \lim_{x \to \infty} g(x) \>?$$
Calculus: Limit at infinity
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calculus