The Sandwich Theorem and a cute little application

The Sandwich Theorem.

Suppose that g(x) \leq f(x) \leq h(x) for all x in some open interval containing c, except possibly at

x=c itself. Suppose also that

\lim_{x \rightarrow c}g(x) = \lim_{x \rightarrow c}h(x)=L.

Then, \lim_{x \rightarrow c}f(x)=L.

Question:

Prove that for any function f, \lim_{x \rightarrow c}|f(x)|=0 implies that

\lim_{x \rightarrow c}f(x)=0.

Hint: Use -|f(x)| \leq f(x) \leq |f(x)|.

Please do send your questions, comments, etc.

More later,

Nalin Pithwa

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