Limits
Description: This quiz covers the fundamental concept of limits in mathematics, focusing on understanding the behavior of functions as their inputs approach specific values. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: limits real analysis calculus |
Given the function (f(x) = \frac{x^2 - 4}{x - 2}), find the limit of (f(x)) as (x) approaches (2).
Evaluate the limit of (\sqrt{x^2 + 1} - x) as (x) approaches (\infty).
Find the limit of (\frac{\sin(3x)}{x}) as (x) approaches (0).
Determine the limit of (\frac{e^{2x} - 1}{x}) as (x) approaches (0).
Evaluate the limit of (\frac{\ln(x + 1)}{x}) as (x) approaches (\infty).
Find the limit of (\frac{x^3 - 8}{x - 2}) as (x) approaches (2).
Determine the limit of (\frac{\tan(2x)}{\sin(3x)}) as (x) approaches (0).
Find the limit of (\frac{\sqrt{x^2 + 9} - 3}{x}) as (x) approaches (\infty).
Evaluate the limit of (\frac{x^2 - 4x + 3}{x - 3}) as (x) approaches (3).
Find the limit of (\frac{\sin^2(x)}{x}) as (x) approaches (0).
Determine the limit of (\frac{\log(x + 1)}{x}) as (x) approaches (\infty).
Find the limit of (\frac{x^3 + 2x^2 - 3x + 4}{x^2 - 1}) as (x) approaches (2).
Evaluate the limit of (\frac{e^{2x} - e^{-2x}}{e^x}) as (x) approaches (\infty).
Find the limit of (\frac{\sqrt{x^2 + 4x + 4} - x}{x + 2}) as (x) approaches (-2).
Determine the limit of (\frac{\sin(x) - x}{x^3}) as (x) approaches (0).