Limit Calculator
Polynomial Limit (ax² + bx + c)
Evaluate the limit of a polynomial as x approaches a value
Rational Limit (ax + b)/(cx + d)
Evaluate the limit of a rational function
Limit at Infinity (ax² + bx)/(cx² + dx)
Evaluate the limit as x approaches infinity
Formula
lim(x→a) f(x) = L | L'Hôpital: lim f/g = lim f'/g' (for 0/0 or ∞/∞)
Frequently Asked Questions
What is a limit in calculus?
A limit describes what value a function approaches as the input approaches some value. lim(x→a) f(x) = L means f(x) gets arbitrarily close to L as x gets close to a.
What is L'Hôpital's Rule?
When a limit gives an indeterminate form (0/0 or ∞/∞), L'Hôpital's Rule states: lim f(x)/g(x) = lim f'(x)/g'(x), provided the latter limit exists.
What are one-sided limits?
A one-sided limit approaches a value from only one direction. lim(x→a⁺) approaches from the right, lim(x→a⁻) from the left. The two-sided limit exists only if both one-sided limits are equal.
You may also need
+
Derivative Calculator
Free derivative calculator. Calculate derivatives of common functions with step-by-step rules shown including power rule, chain rule, and product rule.
Math+
Integral Calculator
Free integral calculator. Calculate integrals using power rule, trig integrals, and definite integrals with step-by-step solutions.
Math+
Taylor Series Calculator
Free Taylor and Maclaurin series calculator. Expand common functions into Taylor series and compute approximations at a given point.
Math