Limit Calculator

These presets use algebraic simplification, known theorems, and standard limit identities to produce exact classroom answers. Unlike numerical methods that estimate by plugging in values close to the limit point, this approach gives the mathematically rigorous result.

Not in this version. This calculator covers the most common limit problems from calculus courses. For arbitrary expressions, use a computer algebra system (CAS) like Wolfram Alpha, Desmos, or a symbolic math library.

The function sin(x)/x is actually undefined at x = 0 (it gives 0/0). However, the limit as x approaches 0 is exactly 1, proven using the squeeze theorem. This is one of the most fundamental limits in calculus.

A removable discontinuity occurs when a function is undefined at a point but the limit exists. For example, (x^2 - 4)/(x - 2) is undefined at x = 2, but after canceling the common factor, the limit is 4. The "hole" in the graph can be "removed" by defining the function value as the limit.

The calculator provides the exact answer with a brief justification for each preset. For full step-by-step derivations with intermediate algebra, working through the problem by hand or using a CAS with step display is recommended.

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.