## m.auld64 Group Title can someone please explain to me why the answer to the following question is -infinity, infinity 2 years ago 2 years ago

1. jaersyn Group Title

ticktock

2. m.auld64 Group Title

$\lim_{x \rightarrow -infinity} (\ln(cbrt(x)))/sinx$

3. m.auld64 Group Title

cbrt = cube root

4. jaersyn Group Title

lnx^(1/3)/sinx = (1/3)lnx / sinx ? i thinkk..

5. m.auld64 Group Title

actually apparently -infinity, infinity is not the correct answer.... wolfram lied so if you help me come to the correct answer

6. satellite73 Group Title

?? $\lim_{x\to -\infty}\frac{\ln(\sqrt[3]{x})}{\sin(x)}$

7. m.auld64 Group Title

ya thats it

8. satellite73 Group Title

makes no sense since you cannot take the log of a negative number

9. myko Group Title

i think should be 0

10. satellite73 Group Title

so there is no limit, as the numerator is undefined if $$x\leq 0$$

11. m.auld64 Group Title

oh crap it is $\lim_{x \rightarrow +infinity}$ sorry....

12. satellite73 Group Title

$$\sin(x)$$ has no limit either as it is periodic and takes on all values between -1 and 1 infinitely often

13. satellite73 Group Title

well still no limit

14. satellite73 Group Title

numerator is going to infinity, but denominator is not going to any specific number as i wrote above.

15. satellite73 Group Title

in other words it swings wildly between large positive and large negative values as sine varies between -1 and 1

16. m.auld64 Group Title

so ultimately its undefined

17. satellite73 Group Title

yes for sure undefined

18. m.auld64 Group Title

so with that being said, anytime sinx is in my denomonator i know that the function must be undefined?

19. myko Group Title

hmm

20. jaersyn Group Title

no

21. satellite73 Group Title

well no, the numerator could go to zero, so the whole thing could go to zero

22. satellite73 Group Title

$\lim_{x\to\infty}\frac{e^{-x}}{\sin(x)}$ for example would be zero

23. m.auld64 Group Title

so are there any good tips and tricks you could tell me to help me understand this sort of material

24. satellite73 Group Title

no tricks really, you have to make sure you know what it going on, and don't for example us l'hopital's rule unless it is applicable, i.e. unless you are in indeterminate form, which you are not here. in your example you do not have $$\frac{\infty}{\infty}$$ and so you cannot use l\hopital and get zero for an answer!

25. m.auld64 Group Title

see im not sure how to determine whether i am in that form or not

26. satellite73 Group Title

plug in the number and check or imagine what happens as x gets large if you are going to infinity

27. satellite73 Group Title

in your example as x gets large so does $$\sqrt[3]{x}$$ and therefore so does $$\ln(\sqrt[3]{x})$$ but the prolem is that sine does not get large and does not have a limit

28. satellite73 Group Title

so basically what i am saying is that in this problem there is no trick or gimmick. you just have to imagine what happens as x gets bigger and bigger

29. m.auld64 Group Title

ok thanks!