Limits & Continuity Solver

About Limits & Continuity

At university level, limits are no longer just "plug the value in and see what happens". The 12 worked problems include the formal epsilon-delta definition (the line a B.Sc student is asked to write on day one of analysis), the common limits worth memorising (sin x / x, (1 + 1/n)ⁿ, (1 − cos x) / x²), L'Hôpital's rule for 0/0 and ∞/∞ forms, and the three conditions a function must satisfy to be continuous at a point. A few problems test continuity of piecewise-defined functions, which is where most students slip.

What this calculator does

• Step-by-step working. Every intermediate line is shown, in the layout examiners reward in CBSE / ICSE and university scripts.
• Graphs where they help. Functions and equations are plotted so you can see the result rather than just read it.
• Verification. The answer is substituted back into the original problem so you know the working is consistent.

Frequently Asked Questions