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Courses / Calculus I / Calc-1 Discussion 02

Identify what Skill is

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Discussion Topics covered: Identify what Skill is needed to solve the limit / Definition of an asymptote and how to identify it

Part A: Classification Matrix (~45 mins)

Instructions: Before solving, classify each problem, identify the governing rule or theorem, and justify your classification using visual clues.

graph TD
    A[Identify Visual Clues] --> B{Form of the function?}
    B -->|Products/Quotients| C[Product/Quotient Rule]
    B -->|Composite functions| D[Chain Rule]
    B -->|Trig/Exponential| E[Special Derivative Rules]
Problem Classification Identifying Rule/Theorem Visual Clues / Justification
1
2
3
4

📅 Problem 1

Identify all vertical and horizontal asymptotes of f(x)=2x2−8x2−9f(x) = \frac{2x^2 - 8}{x^2 - 9}.

Solution to Problem 1

Vertical Asymptotes: Set denominator to 0:

x2−9=0  ⟹  x=±3x^2 - 9 = 0 \implies x = \pm 3
Since the numerator is non-zero at these points, x=3x=3 and x=−3x=-3 are vertical asymptotes. Horizontal Asymptotes: Find limits as x→±∞x \to \pm\infty:
lim⁡x→∞2x2−8x2−9=2\lim_{x \to \infty} \frac{2x^2 - 8}{x^2 - 9} = 2
Therefore, y=2y = 2 is the horizontal asymptote.