Calculus · Practice

Limits — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

Evaluate $\displaystyle\lim_{x \to 2}(x + 3)$ .

Problem 2

Evaluate $\displaystyle\lim_{x \to 2} x^2$ .

Problem 3

Evaluate $\displaystyle\lim_{x \to 1} \frac{x^2 - 1}{x - 1}$ .

Problem 4

Evaluate $\displaystyle\lim_{x \to \infty} \frac{1}{x}$ .

Problem 5

Evaluate $\displaystyle\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$ .

Problem 6

Evaluate $\displaystyle\lim_{x \to \infty} \frac{3x + 1}{x + 2}$ .

Problem 7

Evaluate $\displaystyle\lim_{x \to 0} \frac{\sin x}{x}$ .

Problem 8

Evaluate $\displaystyle\lim_{x \to \infty} \frac{5x + 1}{x^2 + 3}$ .

Problem 9

Evaluate $\displaystyle\lim_{x \to 0} \frac{\sqrt{x + 4} - 2}{x}$ .

Problem 10

Evaluate $\displaystyle\lim_{x \to 0} \frac{\sin 2x}{x}$ .

Problem 11

Evaluate $\displaystyle\lim_{x \to \infty} \frac{x^2 + 5}{x^2 - 3}$ .