University:
Kentucky State University
Course:
MAT 120 | Precalculus
Academic year:

2020
Views:

449

Pages:

1
Author:

Quintin Ware

**Horizontal asymptote** The line y=L is called horizontal asymptote to the line y=f(x), if lim f(x) = L or lim f(x) = L **Ex:** Find a horizontal asymptote. **1. f(x) = 1/x** lim(x→∞) 1/x = 0 lim(x→-∞) 1/x = 0 y = 0 is HA. **2. f(x) = x-3 / 3x+5** lim(x→∞) (x-3) / (3x+5) = 1/3 y = 1/3 is HA as x → ±∞ **3. f(x) = √(4x² + 1) / (2x-3)** lim(x→∞) √(4x² + 1) / (2x-3) = 2 lim(x→-∞) √(4x² + 1) / (2x-3) = -2 y = 2 as x → ∞, y = -2 as x → -∞ **4. f(x) = e^x** lim(x→∞) e^x = ∞ lim(x→-∞) e^x = 0 y = 0 is HA as x → -∞ **5. f(x) = 2 + tan^(-1)(x)** lim(x→∞) 2 + tan^(-1)(x) = 2 + π/2 lim(x→-∞) 2 + tan^(-1)(x) = 2 - π/2 y = 2 + π/2 as x → ∞, y = 2 - π/2 as x → -∞ **6. f(x) = 4x^2 - 1 / 2x + 1** lim(x→∞) (4x^2 - 1) / (2x + 1) = 2x - 1 y = 2x - 1 as x → ±∞