CBSE · Class 6-12

Class 11 · Mathematics (041)

Unit 12 · Class 11Mathematics (041)

Calculus

Limits and Derivatives

Intuitive idea of limits, algebra of limits, and derivative from first principles.

Formative-only for boards

Chain rule for composite functions

Learn these concepts — they won't appear in the CBSE 2026-27 board paper.

Lessons

4 concepts

1
Intuitive Idea of Limit
$\lim_{x \to a} f(x) = L$ means $f(x)$ gets arbitrarily close to $L$ as $x$ approaches $a$ .
2
Standard Limits
$\lim_{x \to 0} \dfrac{\sin x}{x} = 1$ ; $\lim_{x \to 0} \dfrac{1 - \cos x}{x} = 0$ ; $\lim_{x \to a} \dfrac{x^n - a^n}{x - a} = n a^{n-1}$ .
3
Derivative from First Principles
$f'(x) = \lim_{h \to 0} \dfrac{f(x + h) - f(x)}{h}$ .
4
Rules of Differentiation
Sum, product $\left(fg\right)' = f'g + fg'$ , quotient $\left(\dfrac{f}{g}\right)' = \dfrac{f'g - fg'}{g^2}$ .

Skills to practise

Skill · medium

Limits and Derivatives — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.