1. Limits and Continuity

Understanding Limits — Quiz

Test your understanding of understanding limits with 5 practice questions.

Practice Questions

Question 1

Which of the following statements best describes the concept of a limit in calculus?

Question 2

Consider the graph of a function with a vertical asymptote at $x = a$. What can be concluded about the limit of the function as $x$ approaches $a$?

Question 3

When evaluating the limit of a rational function $f(x) = \frac{P(x)}{Q(x)}$ as $x$ approaches $a$, if direct substitution yields the indeterminate form $ \frac{0}{0} $, what is the most appropriate first step to simplify the expression?

Question 4

Evaluate the limit: $$ \lim_{x \to 2} \frac{x^2 - 5x + 6}{x - 2} $$

Question 5

If $ \lim_{x \to c^-} f(x) = L_1 $ and $ \lim_{x \to c^+} f(x) = L_2 $, for the two-sided limit $ \lim_{x \to c} f(x) $ to exist, what must be true?