1. Limits and Continuity

Determining Limits Using The Squeeze Theorem — Quiz

Test your understanding of determining limits using the squeeze theorem with 5 practice questions.

Practice Questions

Question 1

What does the Squeeze Theorem say about the limit of a function $f(x)$ when $g(x) \le f(x) \le h(x)$ near a point and both $g(x)$ and $h(x)$ approach the same value there?

Question 2

Evaluate $\lim_{x\to 0} x^2\sin\left(\frac{1}{x}\right)$ using the Squeeze Theorem.

Question 3

Why does $\lim_{x\to 0} \lvert x\rvert\cos\left(\frac{1}{x}\right)$ exist, and what is its value?

Question 4

Which pair of functions can be used to squeeze $f(x)=x^2\sin(x)$ as $x\to 0$?

Question 5

What must be true about the two bounding functions in the Squeeze Theorem for a limit conclusion to work?