evaluate-the-limit-xxtopminfty-and-identify-any-horizontal-asymptotes-for-the-fu

Question

Evaluate the limit as ﻿x→±∞x	o\pm\inftyx→±∞﻿ and identify any horizontal asymptotes for the function ﻿f(x)=x4−25x2−25f\left(xight)=\frac{$$x^4-25$$}{$$x^2-25$$}f(x)=x2−25x4−25​﻿.

Accepted Answer

﻿lim⁡x→∞f(x)=lim⁡x→−∞f(x)=∞\displaystyle \lim_{x 	o \infty}{f(x)}=\lim_{x 	o -\infty}{f(x)}=\inftyx→∞lim​f(x)=x→−∞lim​f(x)=∞﻿No horizontal asymptotes

Answer

﻿lim⁡x→∞f(x)=lim⁡x→−∞f(x)=−∞\displaystyle \lim_{x 	o \infty}{f(x)}=\lim_{x 	o -\infty}{f(x)}=-\inftyx→∞lim​f(x)=x→−∞lim​f(x)=−∞﻿No horizontal asymptotes

Answer

﻿lim⁡x→∞f(x)=lim⁡x→−∞f(x)=1\displaystyle \lim_{x 	o \infty}{f(x)}=\lim_{x 	o -\infty}{f(x)}=1x→∞lim​f(x)=x→−∞lim​f(x)=1﻿Horizontal asymptote: ﻿y=1y=1y=1﻿

Answer

﻿lim⁡x→∞f(x)=1\displaystyle \lim_{x 	o \infty}{f(x)}=1x→∞lim​f(x)=1﻿; ﻿lim⁡x→−∞f(x)=−1\displaystyle \lim_{x 	o -\infty}{f(x)}=-1x→−∞lim​f(x)=−1﻿Horizontal asymptotes: ﻿y=1y=1y=1﻿ and ﻿y=−1y=-1y=−1﻿

Evaluate the limit as x→±∞x\(\to\[\pm\]\infty\)x→±∞ and identify any horizontal asymptotes for the function f(x)=x4−25x2−25f\(\left\)(x\(\right\))=\(\frac{x^4-25}{x^2-25}\)f(x)=x2−25x4−25.

Evaluate the limit as $x\(\to\[\pm\]\infty\)$ and identify any horizontal asymptotes for the function $f\(\left\)(x\(\right\))=\(\frac{x^4-25}{x^2-25}\)$ .