Verified Calculus Solver with Step-by-Step Explanations

Limit Calculator with Steps

Evaluate two-sided and one-sided limits at finite points or infinity with supported deterministic methods.

Deterministic coreAnimated stepsNo sign-up to try

Dedicated workspace

Limit solver

Engine

Use ^ for powers and parentheses for functions. You can enter sec(x), csc(x), cot(x) and arctan(x) directly; trigonometric inputs use radians.

Input help and supported methods

Keep the original question visible. Confirm the variable and the live preview before calculating. Use ^(1/2) for a square root and explicit parentheses for function arguments.

Choose the approach value and direction. An unsupported limit is not a proof of divergence. Sampling is only a numerical reference.

Read the method

Try one. See the steps.

Click to fill the input. Calculation starts only when you choose Solve.

Live problem preview

Rules you can recognize

How this calculator chooses a method

Direct substitution

lim⁡x→af(x)=f(a)\lim_{x\to a}f(x)=f(a)

Substitute the approach value immediately when the expression is continuous there and produces a finite result.

Simplification and factoring

x2−a2x−a⟶x+a\frac{x^2-a^2}{x-a}\longrightarrow x+a

Factor and cancel the term causing an indeterminate 0/0 form, then evaluate the equivalent simplified expression.

L'Hôpital scenarios

lim⁡fg=lim⁡f′g′\lim\frac{f}{g}=\lim\frac{f^{\prime}}{g^{\prime}}

For supported 0/0 quotients, differentiate the numerator and denominator once before evaluating the limit again.

Three clear moves

How to use this calculator

Enter the approach point and select both sides, left, or right. Continuous expressions use direct substitution; supported indeterminate quotients use a single derivative-based resolution.

Enter one expression using standard mathematical syntax.

Choose the variable and task-specific options.

Review the result, verification note and ordered steps.

Verified means checked, not merely generated

Continue with a related calculator built for a different calculus intent.

DerivativesDifferentiate a single-variable expression or compute a higher-order derivative.IntegralsFind an antiderivative for an expression without finite bounds.Definite integral calculatorUse lower and upper bounds to calculate accumulated change, without + C.Partial fraction calculatorDecompose a rational expression before integration; decomposition alone is not the integral.