Question

lim tan3x/ 3tan2x
x->0

Answer 1

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

Answer 2

0.

Answer 3

the answerr is 1/2

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

expand? what does that mean?

Answer 15

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

Answer 16

okay. thank you very much