Limit of (1-cos(2x²))/(1-cos(3x²)) as x→0

[kira137]

Homework Statement

Find

limit ...(1-cos(2x^2)) / (1-cos(3x^2))
x->0

2. The attempt at a solution
since the above gave me 0/0, I used l'Hopital method..
then i got

(4x)sin(2x^2) / (6x)(sin3x^2)
which gives me 0/0 again..

so I kept on using l'Hopital.. but it seemed on going forever

is there other way to solve this..?
thank you in advance

 

[LCKurtz]

Homework Statement

Find

limit ...(1-cos(2x^2)) / (1-cos(3x^2))
x->0

2. The attempt at a solution
since the above gave me 0/0, I used l'Hopital method..
then i got

(4x)sin(2x^2) / (6x)(sin3x^2)
which gives me 0/0 again..

so I kept on using l'Hopital..

Don't keep using LH rule. Remember you know (at least you should know):

$$\lim_{x\rightarrow 0}\frac {\sin x} x = 1$$

See if you can figure out how to use that next.

 

[phsopher]

Using LH twice doesn't give 0/0.