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7.Calculus – Practice Problems
Class 11 • Mathematics • NCERT
Calculus – Practice Problems
[ Embed Practice Discussion Video Here ]
This practice set helps students strengthen their understanding of Limits and Derivatives as per NCERT Class 11. Problems are designed to build confidence, accuracy, and exam readiness.
Instructions
- Attempt all questions before checking answers.
- Show proper steps in written practice.
- All questions are NCERT-aligned.
A. Limits (Practice)
- Evaluate: limx→2 (3x + 1)
- Evaluate: limx→0 (5x − 7)
- Evaluate: limx→1 (x² + 2x)
- Evaluate: limx→0 (sin x)/x
- Evaluate: limx→0 (1 − cos x)/x²
- Evaluate: limx→0 (sin 4x)/x
- Evaluate: limx→1 (x² − 1)/(x − 1)
- Evaluate: limx→0 (tan x)/x
- Evaluate: limx→0 (ex − 1)/x
- Does limx→0 |x|/x exist?
B. Derivatives from First Principles
- Find the derivative of f(x) = 4 using first principles.
- Find the derivative of f(x) = x using first principles.
- Find the derivative of f(x) = x² using first principles.
- Find the derivative of f(x) = 3x using first principles.
- Find the derivative of f(x) = x² + 1 using first principles.
C. Simple Derivative Rules
- Find d/dx (7x²).
- Find d/dx (5x³ − 3x).
- Find d/dx (x⁴ + x²).
- Find d/dx (6).
- Find d/dx (x³ − 4).
- Find d/dx (2x² + 5x − 1).
- Find d/dx (x).
- Find d/dx (x² − x).
- Find d/dx (10x).
- Find d/dx (x³ + 3x²).
✅ Show Answer Key
Limits
- 7
- −7
- 3
- 1
- 1/2
- 4
- 2
- 1
- 1
- No
First Principles
- 0
- 1
- 2x
- 3
- 2x
Derivative Rules
- 14x
- 15x² − 3
- 4x³ + 2x
- 0
- 3x²
- 4x + 5
- 1
- 2x − 1
- 10
- 3x² + 6x
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