find-the-following-limits-and-identify-the-horizontal-asymptotes-if-any-for-the-

Question

Find the following limits and identify the horizontal asymptotes (if any) for the function $g (x) = \frac{4 x^{2} + 5 x - 3}{2 x^{2} - 7}$ :

$\lim_{x \to \infty} g (x)$

$\lim_{x \to - \infty} g (x)$

Accepted Answer

$\lim_{x \to \infty} g (x) = 2$

$\lim_{x \to - \infty} g (x) = 2$

Horizontal asymptote: $y equals 2$

Answer

$\lim_{x \to \infty} g (x) = 2$ $= \frac{1}{2}$

$\lim_{x \to - \infty} g (x)$ $= - \frac{1}{2}$

Horizontal asymptotes: $y equals 2$ and $y = - 2$

Answer

$\lim_{x \to \infty} g (x) = 2$ $= \frac{1}{2}$

$\lim_{x \to - \infty} g (x)$ $equals 1$

Horizontal asymptote: $y = - 1$

Answer

$\lim_{x \to \infty} g (x) = 2$ $= \frac{1}{2}$

$\lim_{x \to - \infty} g (x)$ $= - 1$

No horizontal asymptote

Find the following limits and identify the horizontal asymptotes (if any) for the function g(x)=4x2+5x−32x2−7g\left(x\right)=\frac{4x^2+5x-3}{2x^2-7}: limx→∞g(x)\lim_{x\rightarrow\infty}g\left(x\right)limx→−∞g(x)\lim_{x\rightarrow-\infty}g\left(x\right)