## swin2013 2 years ago Determine the limit

1. swin2013

$\lim x-> 0 \frac{ 3\sin4x }{ \sin3x }$

2. swin2013

sorry that's limit approaching zero lol

3. hartnn

so do u know the basic limit of sin x/x =... ?

4. swin2013

yes it's = 1?

5. hartnn

so, according to that formula , u need the denominator same as angle of sin. so, multiply and divide by 4x in numerator and multiply and divide by 3x in denominator

6. hartnn

$$\huge \lim \limits_{x-> 0} \frac{ 3 \frac{4x.\sin4x}{4x} }{ 3x.\frac{\sin3x}{3x} }$$

7. zepdrix

That seems like a bit of overkill hart :o don't you just need 4x/4x?

8. hartnn

yeah, thats correct, but i wanted to brig out the point that whenever you see sin ax , multiply and divide by ax

9. swin2013

well can i bring out what's in the denominator first?

10. swin2013

by multiplying the denominator by 3?

11. zepdrix

$\large \lim_{x \rightarrow 0}\frac{4x}{4x}\frac{3\sin4x}{\sin3x} \quad = \quad 4\lim_{x \rightarrow 0}\frac{\sin4x}{4x}\frac{3x}{\sin3x}$

12. zepdrix

Oh ok i see what you meant :)

13. zepdrix

The upside down one will also give you 1 swin.

14. zepdrix

It might make more sense if you look at the way hart wrote it out.

15. hartnn

yeah, lim x->0 x/sin x also equals 1

16. swin2013

chyea I'm trying to find a quicker way to solve for my final hahaha! i initially split them up so it was 3sin4x/1 * 1/sin3x. I'm not sure if that's legal

17. hartnn

yeah, its legal step, but you will still need the form sin x/x so you need to multiply and divide by the angle of sin

18. swin2013

So it will be 4?

19. zepdrix

$\large \color{green}{Good}\quad \color{blue}{job!}$

20. swin2013

Lol thanks guys!! A couple of hours till I take my final :)

21. zepdrix

Oooo exciting! :O keep cramming. Sleep is good also.

22. hartnn

do u need to show steps ?

23. hartnn

because if you do, while taking the limit, you also need to show that 3x->0 and 4x-> 0

24. swin2013

Probably not, because I think it's just simplifying it to make sinx/x = 1. But I understand how you solved it, Thanks for the review :)

25. hartnn

ok, welcome ^_^