Calculus 1
Master the fundamentals of calculus: limits, derivatives, and their applications.
Organize your study notes with MindMapFlow and drill core derivative facts using spaced repetition in FlashForge.
📍 Limits and Continuity
Limits describe the behavior of functions as they approach specific points. Understanding limits is essential for calculus.
Key Concepts:
- • Limit definition and notation: limx→a f(x)
- • One-sided limits (left and right)
- • Infinite limits and limits at infinity
- • Continuity and discontinuities
📈 Derivatives
The derivative measures how a function changes as its input changes. It's the fundamental tool for analyzing rates of change.
Differentiation Rules:
- • Power Rule: d/dx[xn] = nxn-1
- • Product Rule: d/dx[f·g] = f'g + fg'
- • Quotient Rule: d/dx[f/g] = (f'g - fg')/g²
- • Chain Rule: d/dx[f(g(x))] = f'(g(x))·g'(x)
🎯 Applications of Derivatives
Derivatives have powerful real-world applications in optimization, curve sketching, and motion analysis.
Key Applications:
- • Finding critical points (maxima and minima)
- • Curve sketching and concavity
- • Optimization problems (max/min values)
- • Related rates (how variables change together)
- • Linear approximation and differentials
⚡ Related Rates
Related rates problems involve finding the rate at which one quantity changes by relating it to other quantities whose rates are known.
Common Problems:
- • Ladder sliding down a wall
- • Water draining from a tank
- • Shadow length changing
- • Balloon inflating/deflating
Visualize related rates problems with MindMapFlow to identify relationships between variables before solving.
🎓 Ready to Practice?
Use our interactive calculators to solve calculus problems and see step-by-step solutions.