Example 1
Find lim as x -> 3 of (x^2 - 9)/(x - 3)A removable 0/0 form simplified by factoring.
Limit Solver
Purpose-built solver page
Limit Solver
Use this limit solver for step-by-step reasoning about finite, one-sided, infinite, and indeterminate limits. Include the approach point and direction so the response addresses the correct limit.
Type or upload a problemWorked explanationsNo sign-up required
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lim x→a f(x)
Direct-substitution limits
One-sided limits
Limits at infinity
limit solver
Solve your limit problem
Enter your limit problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
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limit solver
What this Limit solver is designed for
The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.
Direct-substitution limits
limₓ→ₐ f(x) = f(a)Check continuity and evaluate the expression when substitution is valid.
One-sided limits
limₓ→ₐ⁻ f(x) · limₓ→ₐ⁺ f(x)Compare behavior from the left and right before claiming a two-sided limit.
Limits at infinity
limₓ→±∞ f(x)Analyze dominant terms and long-run behavior.
Indeterminate forms
0/0 · ∞/∞Simplify, factor, rationalize, use identities, or apply a theorem only when its conditions hold.
Step
How to use the Limit solver
A complete prompt usually produces a more useful explanation than an isolated expression.
- 1
State the approach
x → a⁻ · x → a⁺ · x → ±∞Include the variable, target value, and left/right direction when needed.
- 2
Try direct substitution
f(a)Identify whether the result is a value, undefined expression, or indeterminate form.
- 3
Choose a justified method
0/0 → factor · rationalize · identityFactor, rationalize, compare dominant terms, or use a valid theorem.
- 4
Check behavior
L⁻ = L⁺ ⇒ LCompare one-sided behavior or nearby values when useful.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
Example
Limit problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 2
Find lim as x -> 0+ of ln(x)A one-sided limit with unbounded behavior.
Example 3
Find lim as x -> infinity of (4x^2 + 1)/(2x^2 - 3x)A rational limit controlled by leading terms.
Common mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Treating 0/0 as the answer
It is an indeterminate form that signals more analysis is needed.
Ignoring one-sided behavior
A two-sided limit exists only when the left and right limits agree.
Using L'Hôpital automatically
The rule requires a suitable indeterminate quotient and differentiability conditions.
Limit solver FAQ
