High School Limit Calculator (L’Hôpital’s Rule)
Evaluate limits of rational functions f(x)/g(x) as x &to; c.
Supports standard math functions: sin, cos, ln, sqrt, etc.
Limit Result
Step-by-Step Analysis
Function Graph
Understanding the Limit Calculator (L’Hôpital’s Rule)
In calculus, a limit describes the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential for defining continuity, derivatives, and integrals. Sometimes, simply plugging in the target value results in a valid number. However, often we encounter “Indeterminate Forms.”
Indeterminate Forms
If you evaluate a limit lim(x→c) f(x)/g(x) and get results like 0/0 or ∞/∞, you cannot conclude the answer is 0, 1, or infinity. It is “indeterminate,” meaning the limit depends on how fast the numerator and denominator are approaching 0 or infinity relative to each other.
L’Hôpital’s Rule
This powerful rule states that if a limit yields an indeterminate form (0/0 or ∞/∞), the limit of the ratio of functions is equal to the limit of the ratio of their derivatives.
Why use a Limit Calculator (L’Hôpital’s Rule)?
Calculating derivatives manually can be tedious and prone to error, especially for complex composite functions involving trigonometry or logarithms. This tool automates the differentiation process, checks if the conditions for the rule are met, and computes the final value, helping you verify your calculus homework steps.
FAQ
Yes, this is a free educational tool accessible directly in your browser.
If the function approaches different values from the left and right, or grows without bound (not in an indeterminate way), the limit may be “Undefined” or “Infinity”.
Yes. If applying the rule once still results in 0/0, you can take the derivative again (second derivative) until a determinate form is reached.
This tool calculates the general two-sided limit. If the left and right behavior differ significantly, visual inspection of the graph provided is recommended.