Mathematics · Class 11
Limits and Derivatives
Learn Limits and Derivatives with notes, examples, and practice questions.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Limits describe approaching behaviour; derivatives are limits of difference quotients. Gateway to Class 12 calculus.
Limits
lim xⁿ
as x→a: aⁿ
0/0 forms
Factorise, rationalise, standard limits
lim sin x/x
= 1 as x→0
lim (1+x)^(1/x)
= e as x→0
Derivatives
Definition
f′(x) = lim[h→0] [f(x+h)−f(x)]/h
Power rule
d/dx xⁿ = nxⁿ⁻¹
Standard
(sin x)′=cos x; (cos x)′=−sin x; (eˣ)′=eˣ
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
lim (x²−4)/(x−2)
x→2.
- 1(x−2)(x+2)/(x−2)=x+2
- 2→4
Answer
4
Derivative of x³
From first principles or rule.
- 13x²
Answer
3x²
Key Points to Remember
- ✓ Left-hand and right-hand limits must match
- ✓ Differentiability implies continuity
- ✓ Chain rule preview for composites
Exam Tips
- • Use standard limits table
- • Show limit steps for 0/0
Practice MCQs — Limits and Derivatives
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
lim(x→0) sin x/x =