1. Limits and Continuity

One-sided Limits — Quiz

Test your understanding of one-sided limits with 5 practice questions.

Practice Questions

Question 1

For the function $f(x) = \begin{cases} 3x + 1 & \text{if } x < 1 \\ 2x & \text{if } x \ge 1 \end{cases}$, what is $\lim_{x \to 1^-} f(x)$?

Question 2

What can be concluded if $\lim_{x \to a^-} f(x) = 2$ and $\lim_{x \to a^+} f(x) = 3$?

Question 3

Consider the function $f(x) = \frac{x^2 - 1}{x - 1}$. What is $\lim_{x \to 1^-} f(x)$?

Question 4

For the function $g(x) = \begin{cases} x^2 & \text{if } x < 2 \\ 3 & \text{if } x \ge 2 \end{cases}$, what is $\lim_{x \to 2^+} g(x)$?

Question 5

If a function has a jump discontinuity at $x = c$, what can be said about its one-sided limits?