Question

Identify the oblique asymptote of f(x) = quantity 2 x squared plus 3 x plus 8 over quantity x plus 3.

Answer 1

The oblique asymptote in the slope-intercept form is:
y = m x + b,  where:
m = $\lim_{x \to \infty} \frac{ 2x^{2}+3x+8}{ x^{2} +3x}$ = 2
b = $\lim_{x \to \infty} \frac{ x^{2} +3x+8}{x+3} - 2 x = \\ \lim_{x \to \infty} \frac{2 x^{2} + 3 x + 8 - 2 x^{2} -6x}{x+3}= \\ \lim_{x \to \infty} \frac{-3x+8}{x+3}$ = -3
Answer:  y = 2 x - 3