1. Evaluating Limits Analytically: Factoring, rationalizing conjugates, and simplifying complex fractions.
  2. Limits Involving Infinity: Extracting horizontal and vertical asymptotes mathematically.
  3. Continuity & Types of Discontinuities: Point (hole), jump, and infinite discontinuities.
  4. The Intermediate Value Theorem (IVT): Formally proving the existence of roots within closed intervals.
  5. The Limit Definition of the Derivative: Evaluating $\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$ step-by-step.

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