Lemma 7.1.10. Let U ⊂ℝ, p be a limit point of U, f: U →ℝ, and L ∈ℝ. Then limx → p f(x) = L if an

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Lemma 7.1.10. Let $U \subset \mathbb{R}$, $p$ be a limit point of $U$, $f: U \to \mathbb{R}$, and $L \in \mathbb{R}$. Then $\lim_{x \to p} f(x) = L$ if and only if $\lim_{x \to p} (f(x) - L) = 0$