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[Step-by-Step] Let f, g, and h be functions from D into R, and let c be an accumulation point of $D .$ Suppose that f(x) ≤q g(x) ≤q h(x), for all

Question: Let f, g, and $h$ be functions from $D$ into $\mathbb{R}$, and let $c$ be an accumulation point of $D .$ Suppose that $f(x) \leq g(x) \leq h(x)$, for all $x \in D$ with $x \neq c$, and suppose $\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow c} h(x)=L$. Prove that $\lim _{x \rightarrow c} g(x)=L$.

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[Step-by-Step] Let f, g, and h be functions from D into R, and let c be an accumulation point of $D .$ Suppose that f(x) ≤q g(x) ≤q h(x), for all

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