Calculus Notes
1. Limits and Continuity
- Limit of a Function: lim_{x -> a} f(x) = L
- One-sided Limits
- Limit Laws (Sum, Product, Quotient)
- L'Hpital's Rule: Used when limits result in indeterminate forms like 0/0 or infinity/infinity
- Continuity: A function is continuous at x = a if lim_{x -> a} f(x) = f(a)
2. Derivatives
- Definition: f'(x) = lim_{h -> 0} [f(x+h) - f(x)] / h
- Rules:
- Power Rule: d/dx[x^n] = nx^{n-1}
- Product Rule: (fg)' = f'g + fg'
- Quotient Rule: (f/g)' = (f'g - fg') / g^2
- Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)
- Applications:
- Tangents and Normals
- Maxima and Minima
- Increasing/Decreasing Functions
- Concavity and Inflection Points
3. Integration
