📈 Continuity & Differentiability Simulator
CalculusWhat's happening? A function is continuous if limit = value. Differentiable if derivative exists (smooth, no sharp corners). Differentiable → continuous, but not vice versa!
Continuity & Differentiability is a core concept tested across JEE Main and Advanced.
Understanding this concept visually builds the intuition you need to solve numerical problems faster and avoid common mistakes.
Key formula
Continuity & Differentiability Formula
Core Formula
f'(a) = lim(h→0) [f(a+h)-f(a)]/h
Adjust the controls above and watch how changing each variable affects the result in real time.
JEE Application
This concept appears in both numerical and conceptual questions. Master the formula and the visual intuition together.
Step-by-step
How to approach Continuity & Differentiability problems
- Identify the variables — list what's given and what's asked.
- Apply the core formula — f'(a) = lim(h→0) [f(a+h)-f(a)]/h.
- Check units — convert to SI units before calculating.
- Verify with intuition — does the answer make mathematical sense?
FAQs
Continuity & Differentiability Questions
How does this concept appear in JEE?
Expect 1-2 questions per paper. Focus on understanding the relationship between variables visually.
What's the most common mistake?
Memorizing formulas without understanding the visual intuition. Build both.