Question

Can you help me please :
lim cot(2x)/cot(3x) as x approaches to 0

Answer 1

can u draw the problem please

Answer 2

@dan815 @Michele_Laino @amistre64

Answer 3

find the limit of cot(2x)/cot (3x) as x approaches to 0 @israa88

Answer 4

cos(2x)sin(3x)
--------------
sin(2x)cos(3x)

we might be able to modify these if need be to get them into a more familiar form

Answer 5

\[\lim_{x \rightarrow 0} \tan(3x)\cot(2x)\] I guess you can use L' hopital rule

Answer 6

sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
sin(a-b) = sin(a)cos(b) - sin(b)cos(a)
---------------------------------

sin(a+b) + sin(a-b) = 2 sin(a)cos(b)

1/2 (sin(a+b) + sin(a-b)) = sin(a)cos(b)

Answer 7

sin(3x)cos(2x)
-----------
sin(2x)cos(3x)



sin(5x) + sin(x)
-------------
sin(5x) - sin(x)

Answer 8

just trying out some manipulations:



sin(5x) + sin(x) - sin(x) + sin(x)
----------------------------
sin(5x) - sin(x)



2sin(x)
1 + -------------
sin(5x) - sin(x)

Answer 9

thank you so much @amistre64

Answer 10

any of this seem useful to you? its in sin so we might be able to modify it more with like 5x and x stuff

Answer 11

I'll try it later .. anyway thanks :) @amistre64

Answer 12

\[\huge \lim_{x \rightarrow 0} \frac{ \cot(2x) }{ \cot(3x) } = \lim_{x \rightarrow 0} \tan(3x)(\cot(2x)) \]

You can set it up as 0/0, just another method if you want to check.

Answer 13

might not have had to go as far as i did, the simple sin cos definintions might be useful

cos(2x)sin(3x)
--------------
sin(2x)cos(3x)


2x 3x cos(2x)sin(3x)
-----------------
2x 3x sin(2x)cos(3x)


3x cos(2x)
----------
2x cos(3x)

Answer 14

That's even better actually :)

Answer 15

yeah ...

Answer 16

we got the results now? :)

Answer 17

cos(2x) and cos(3x) to 1

x/x to 1

leaving ..... tada lol

Answer 18

:) Voila ! @amistre64