## bobobobobb 3 years ago lim tan3x/ 3tan2x x->0

1. brainshot3

Is it zero? Separate the two and multiply out. It is either zero or indeterminate, but I'd go with zero.

2. liliy

0.

3. bobobobobb

4. yash007

use l' hospital rule and u'll get 1/2

5. brainshot3

Just checked it on Wolfram Alpha. The answer is 0.

6. vi3tbloodxx

Using the l'Hôpital's rule: Take derivative of the top and the bottom: tan3x = 3sec²3x 3tan2x = 6sec²2x So its: 3sec²3x/6sec²2x Now plug in x=0 You'll get 3(1)/6(1) = 3/6 =1/2

7. bobobobobb

Thanks all for your help. Any solution without that rule for now? Because the teacher said that we should be able to do this question without any rules. I wasnt taught l'hopitals rule yet

8. yash007

then using trigonometic formulaes u can xpand it and then u'll get what u want...:) all d best..:)

9. liliy

@bobobobobb so then i'm gonna have to say, go with zero

10. brainshot3

It would be zero. Divide and conquer; veni vidi vici. Tan... * tan... will both go to zero, multiply out and you will get zero.

11. yash007

no i just solved it with trigonometric formulaes i'm getting 1/2

12. bobobobobb

the answer key says 1/2 but i dont know how

13. yash007

see in numerator u xpand tan 3x and do the same for 6tan 2x in denominator and then put x=0 and u'll get 1/2

14. bobobobobb

expand? what does that mean?

15. yash007

means apply formula for tan 3x and u'll get everything in tan x same u do in denominator and then put x=0 to get ur result

16. bobobobobb

okay. thank you very much