Limit calculator, with the working

Each answer comes with the rule used at every step, written out in full, and a graph of the function next to its derivative, its antiderivative or the point the limit approaches. Everything is worked out in your browser.

Integrals

Indefinite integrals use the power rule, the standard table of exponential, logarithm and trigonometric integrals, substitution, integration by parts, trigonometric identities and partial fractions. Every antiderivative is checked by differentiating it again before it is shown. Some functions, such as e^x² or sin(x)/x, have no antiderivative made of ordinary functions; you are told so plainly. Add bounds, including inf, for a definite integral: the exact value is given when one exists, otherwise a numeric value, and improper integrals that blow up are reported as divergent.

Derivatives

Derivatives show the sum, constant multiple, power, product, quotient and chain rules one at a time, along with the derivatives of exponentials, logarithms, trigonometric and inverse trigonometric functions. Choose a higher order for second or third derivatives, or give a value to evaluate the derivative at a point.

Limits

Limits start with direct substitution. When that gives 0/0 or ∞/∞, the working factors and cancels, compares the highest powers, multiplies by a conjugate or applies L’Hôpital’s rule. Forms like 0·∞, ∞−∞ and 1^∞ are rewritten first. One-sided limits are supported, and a two-sided limit whose sides disagree is reported as not existing.

Typing functions

Write powers with ^, like x^3 or e^(2x). Square roots are sqrt(x), natural logs are ln(x) or log(x), and log10(x) is base 10. Inverse functions are arcsin, arccos and arctan. Other letters, such as a or k, are treated as constants in derivatives and integrals.