6. Sequences and Calculus Intro

Limits Concept — Quiz

Test your understanding of limits concept with 5 practice questions.

Practice Questions

Question 1

Consider the function $f(x) = \frac{\sqrt{x + 1} - 1}{x}$. What is the limit of $f(x)$ as $x$ approaches 0?

Question 2

Given the function $f(x) = \begin{cases} ax + 3 & \text{if } x < 2 \\ x^2 - 1 & \text{if } x \geq 2 \end{cases}$. For what value of $a$ does $\lim_{x \to 2} f(x)$ exist?

Question 3

If $\lim_{x \to c} f(x) = L$ and $\lim_{x \to c} g(x) = M$, and $M \neq 0$, which of the following is always true?

Question 4

Consider the function $f(x) = \frac{|x - 3|}{x - 3}$. What is the value of $\lim_{x \to 3^+} f(x)$?

Question 5

Numerically, if you are trying to estimate $\lim_{x \to 2} f(x)$, which set of $x$-values would provide the most accurate estimation?