## anonymous 4 years ago Compute lim x->0 (4x/sin(3x)+x/cos(3x))

1. myininaya

$\lim_{x \rightarrow 0}(\frac{4x}{\sin(3x)}+\frac{x}{\cos(3x)}=\frac{4}{3}\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}+\lim_{x \rightarrow 0}\frac{x}{\cos(3x)}$ Recall $\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1$

2. myininaya

the other one is just direct sub.

3. anonymous

i didnt quite understand what you just showed =/

4. myininaya

Nothing?

5. anonymous

okay so what did you do their when you put 4/3

6. myininaya

4/3 * 3 =4 I just multiplied the first fraction by 3/3

7. anonymous

which became 12x/sin(9x)?

8. myininaya

oh no

9. myininaya

3sin(3x) does not equal sin(9x)

10. anonymous

oh ur right lol sorry about that

11. anonymous

whats the purpose of multiplying by 3/3?

12. myininaya

$\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1$ Do you recall this?

13. anonymous

i dont

14. myininaya

so this means we can say $\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}=1$

15. anonymous

alright

16. myininaya

so I wanted a 3 up there in our problem

17. myininaya

but if i put a 3 on top I have to put a 3 on bottom

18. anonymous

yes

19. myininaya

so that is why I multiplied by 3/3

20. anonymous

i get it so the first part became 1

21. myininaya

yes 4/3 times 1 is the first part

22. myininaya

not the second part we just plug in 0

23. myininaya

now*

24. myininaya

is everything ok? you got it?

25. anonymous

im writing it down

26. myininaya

ok

27. anonymous

so then it would be 0/cos(3(0))

28. myininaya

0/1=0

29. myininaya

yes

30. myininaya

so we have 4/3 from the first part+ 0 from the second part =4/3

31. anonymous

oh got it thanks!

32. myininaya

:)

33. myininaya

Spikey I appreciate that you want to learn this stuff. Thanks for engaging in the learning process. That is really cool dude.

34. anonymous

lol thank you :) i take AP calc

35. anonymous

in highschool

36. myininaya

Go you! :)

37. myininaya

It is really cool to have that attitude. You will go far.

38. anonymous

theres just some stuff that i dont really comprehend my teacher doesnt teach some stuff clearly

39. anonymous

lol yeah i never give up. :)

40. anonymous

always trying to learn new things.

41. myininaya

Good luck to you and peace out!

42. anonymous

lol bye