Lit Calculus
Explore the fundamentals of calculus in this comprehensive 7-hour course. Begin with an introduction to Zeno's Paradox and delve into the definition of limits, including right- and left-hand limits. Examine vertical asymptotes, limit laws, and the Squeeze Theorem. Study continuity, the Intermediate Value Theorem, and rates of change. Master the limit definition of derivatives and learn various derivative rules, including power, sum/difference, product, and quotient rules. Investigate derivatives of trigonometric, exponential, and logarithmic functions. Tackle implicit differentiation, logarithmic differentiation, and derivatives of inverse trigonometric functions. Explore function extrema, concavity, and graph sketching techniques. Apply L'Hospital's Rule to various indeterminate forms and solve optimization problems involving closest points, largest rectangles, boxes, and cone cups.