Practice Squeeze Theorem in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
If g(x) \leq f(x) \leq h(x) near x = a, and \lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L, then \lim_{x \to a} f(x) = L.
If f is squeezed between two functions that both approach the same value L, then f has no choice—it must also approach L. Like being caught between two walls closing in to the same point.
Example 1
easyUse the squeeze theorem to find \displaystyle\lim_{x \to 0} x^2 \sin\!\left(\frac{1}{x}\right).
Example 2
hardUse the squeeze theorem to prove \displaystyle\lim_{x \to 0} \frac{\sin x}{x} = 1.
Example 3
easyFind \displaystyle\lim_{x \to 0} x\cos\!\left(\frac{1}{x}\right).
Example 4
mediumShow that \displaystyle\lim_{n\to\infty} \frac{\sin n}{n} = 0.