f-x-x-1-x-2-9-find-the-horizontal-asymptote-

Question Number 170812 by MathsFan last updated on 31/May/22

f (x) = \frac{x + 1}{\sqrt{x^{2} + 9}}

find the horizontal asymptote

Answered by Mathspace last updated on 31/May/22

{l i m}_{x \to - \infty} f (x) = {l i m}_{x \to - \infty} \frac{x + 1}{∣ x ∣ \sqrt{1 + \frac{9}{x^{2}}}}

= {l i m}_{x \to - \infty} \frac{x + 1}{- x \sqrt{1 + \frac{9}{x^{2}}}}

= - 1 \Rightarrow y = - 1 i s a s s y m t o t e

a t - \infty

{l i m}_{x \to + \infty} f (x) = {l i m}_{x \to + \infty} \frac{x + 1}{x \sqrt{1 + \frac{9}{x^{2}}}}

Commented by Mathspace last updated on 31/May/22

= 1 \Rightarrow y = 1 i s a s s y m p t o t e a t + \infty