← GSEB Class 11
Limits and Derivatives
Chapter Overview
The limit of f(x) as x approaches a is the value f(x) approaches arbitrarily closely. Standard limits include trigonometric, exponential, and rational functions. The derivative is defined as the limit of the difference quotient and represents instantaneous rate of change or slope of tangent.
The chapter covers first principles of differentiation, standard derivative formulas, and algebra of derivatives (sum, product, quotient rules).
Topics Covered
- Concept of Limits
- Limit Evaluation
- Standard Limits
- Definition of Derivative
- First Principle
- Standard Derivatives
- Algebra of Derivatives
- Geometric Meaning
Key Formulas
limtheta->0 sin(theta)/theta = 1
f'(x) = limh->0 (f(x+h)-f(x))/h
ddx(xn) = nxn-1
ddx(sin x) = cos x
ddx(ex) = ex
Real-World Applications
Applications: Physics (motion), engineering (optimization), economics (marginal analysis), machine learning (gradient descent).
Study Tips
Tip: Master the first principle
Tip: Practice factorization for limit evaluation
Tip: Learn all standard derivative formulas