Question

Horizontal asymptote

Answer 1

take x^8 common from both denom and num and you will be left with 12/4

Answer 2

\[\large \lim_{x\to\infty}\frac{12x^8-6}{3x^8-2x^7}
=\lim_{x\to\infty}\frac{x^8(12-6/x^8)}{x^8(3-2/x)}=
\lim_{x\to\infty}\frac{12-6/x^8}{3-2/x} \]

Answer 3

got it?

now use the fact that for all n
\[\large \lim_{x\to\infty}\frac{K}{x^n}=0 \]

Answer 4

so, the answer would be 4? so it has a horizontal asymptote?

Answer 5

yes
\[\large \lim_{x\to\infty}\frac{12-6/x^8}{3-2/x}=\frac{12-0}{3-0}=4\]
so y=4 is a horizontal asymptote

Answer 6

okay thank you! :D

Answer 7

u r welcome