## anonymous one year ago Which of the following shows that f(x) grows faster than g(x)? the limit as x goes to infinity of f(x)/g(x) = 1000 the limit as x goes to infinity of f(x)/g(x) = 0 the limit as x goes to infinity of f(x)/g(x) = infinity None of these

1. SolomonZelman

2. anonymous

i dot quite recall the rule, i think it was something like if they equal a finite non zero number they grow at the same rate but i don't remember what infinity and zero ment

3. anonymous

so i know its not A , and probably not D

4. SolomonZelman

lets think of this logically. if $$\large\displaystyle \lim_{ x~\rightarrow \infty}~(~f(x)~/~g(x)~)=0$$ then g(x) is growing faster and that is why when you divide f(x) by g(x) you get zero because g(x) is being larger and larger....

5. SolomonZelman

So it is definitely not B.

6. SolomonZelman

right, or disagree ?

7. anonymous

i see your logic , i totally agree :D

8. SolomonZelman

ok, good

9. anonymous

thanks for the help !

10. SolomonZelman

are we done?

11. anonymous

yep , its clearly C

12. SolomonZelman

Good!!

13. SolomonZelman

$$\large\displaystyle \lim_{ x~\rightarrow \infty}~(~f(x)~/~g(x)~)=\infty$$

14. SolomonZelman

yw

15. anonymous

:D

16. SolomonZelman

Have you done LHospitals rule yet? just curious...