1. **Day 1: Fundamentals and Limits** - Review basic concepts of calculus: functions, limits, and continuity. - Practice problems on limits including precise definition of limits (e.g., lim $x \to \sqrt{3} \frac{1}{x^2} = \frac{1}{3}$). - Study properties of functions and continuity analytically and graphically. 2. **Day 2: Differentiation and Applications** - Learn differentiation rules and techniques. - Solve real-life application problems involving rates of change (e.g., rate of distance change of rocket). - Practice finding equations of tangent and normal lines to curves. 3. **Day 3: Curve Sketching and Asymptotes** - Analyze functions for extrema, concavity, and points of inflection. - Study curve sketching using derivatives. - Identify vertical, horizontal, and oblique asymptotes of rational functions. 4. **Day 4: Integration and Riemann Sums** - Understand definite and indefinite integrals. - Practice Riemann sums and limits to find areas under curves. - Solve problems involving area between curves and convergence/divergence of integrals. 5. **Day 5: Advanced Applications and Geometry** - Study length of curves and volume of solids of revolution. - Practice problems on curve length and volume by rotation. - Review analytical geometry concepts related to curves and their properties. This plan balances theory, problem-solving, and application to prepare effectively for calculus and analytical geometry topics in 5 days.