Calc-1 Discussion 02 | Tony's Intertwingled Memex

Discussion Topics covered: Distributive limit laws, resolving indeterminate forms (0/0), infinite limits and vertical asymptotes, limits at infinity and horizontal asymptotes, trigonometric identities, solving and bounding double inequalities, evaluating trigonometric functions at special angles

Part A: Review This Week's Lecture Topics (~30 mins)

Evaluating Limits with Algebraic Techniques & Indeterminate Forms

Applying distributive Limit Laws (sum, difference, constant multiple, product, quotient, and power/root) when individual component finite limits exist
Evaluating left- and right-hand limits at piecewise domain boundaries to verify two-sided limit existence
Resolving $\frac{0}{0}$ indeterminate forms by factoring polynomials or using polynomial long division to isolate and cancel common zero-inducing factors $(x - a)$
Rationalizing numerators and denominators using radical conjugates to resolve $\frac{0}{0}$ indeterminate forms

Infinite Limits, Limits at Infinity, and Asymptotes

Distinguishing vertical asymptotes ( $\frac{c}{0}$ where $c \neq 0$ ) from removable discontinuities / holes ( $\frac{0}{0}$ )
Performing directional signed zero analysis ( $0^+$ vs. $0^-$ ) to evaluate one-sided limits diverging to $+\infty$ or $-\infty$
Evaluating end-behavior limits at infinity ( $\lim_{x \to \pm\infty} f(x)$ ) using leading-term growth dominance to find horizontal asymptotes
Resolving $\infty - \infty$ indeterminate radical forms at infinity and accounting for the sign change $\sqrt{x^2} = |x| = -x$ as $x \to -\infty$

Part B: Next Week's Prerequisite Refresher (~30 mins)

Review the following prerequisite skills:

Part C: General Q/A

Open the floor to questions from students regarding any topic