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)=4x2+5x−32x2−7g\left(x\right)=\frac{$$4x^2+5x-3$$}{$$2x^2-7$$}: lim⁡x→∞g(x)\$$lim_{x\rightarrow\infty}g$$\left(x\right)lim⁡x→−∞g(x)\$$lim_{x\rightarrow-\infty}g$$\left(x\right)

Accepted Answer

lim⁡x→∞g(x)=2\$$lim_{x\rightarrow\infty}g$$\left(x\right)=2lim⁡x→−∞g(x)=2\$$lim_{x\rightarrow-\infty}g$$\left(x\right)=2Horizontal asymptote: y=2y=2

Answer

lim⁡x→∞g(x)\$$lim_{x\rightarrow\infty}g$$\left(x\right) =12=\frac12lim⁡x→−∞g(x)\$$lim_{x\rightarrow-\infty}g$$\left(x\right) =−12=-\frac12Horizontal asymptotes: y=2y=2 and y=−2y=-2

Answer

lim⁡x→∞g(x)\$$lim_{x\rightarrow\infty}g$$\left(x\right) =1=1lim⁡x→−∞g(x)\$$lim_{x\rightarrow-\infty}g$$\left(x\right) =1=1 Horizontal asymptote: y=−1y=-1

Answer

lim⁡x→∞g(x)\$$lim_{x\rightarrow\infty}g$$\left(x\right) =1=1 lim⁡x→−∞g(x)\$$lim_{x\rightarrow-\infty}g$$\left(x\right) =−1=-1 No horizontal asymptote