Question

examples of funtions for:
1. lim x to infinity f(x)/g(x) = infinity
2. lim x to infinity f(x)/g(x) = 6
3. lim x to infinity f(x)/g(x) = 0

Answer 1

\[\lim_{x\to \infty}\frac{f(x)}{g(x)}=\infty\] take any polynomial for the numerator whose degree is larger than the degree of the denominator

Answer 2

you can use
\[\frac{x^2+2}{x}\] or anything of your choosing

Answer 3

Thank you!

Answer 4

\[\lim_{x \rightarrow \infty} \frac{f(x)}{g(x)}=6; \lim_{x \rightarrow \infty} \frac{6x+7}{x+9}=6\]