## Star 5 years ago the limit as x-> 0 for cos(2x)-1 / cos(3x)-1

1. myininaya

ok if you plug in 0 you get 0/0 so you can use l'hospital's rule -2sin(2x)/-3sin(3x) give me just a sec i'm going to use the equation thingy

2. myininaya

$\lim_{x \rightarrow 0}\frac{2}{3} \frac{\sin(2x)}{2x}\frac{\sin(3x)}{3x}6x^2$

3. myininaya

2/3(1)(1)(6)(0)=0

4. star

it says the answer is 4/9

5. myininaya

$\lim_{x \rightarrow 0} \frac{\cos(2x)-1}{\cos(3x)-1}$

6. myininaya

is that right?

7. star

yep

8. myininaya

ok let me see

9. myininaya

oops i see a mistake

10. myininaya

i put sin(3x) in the numerator do you see that?

11. myininaya

$\lim_{x \rightarrow 0}\frac{2}{3}\frac{\sin2x}{2x}\frac{3x}{\sin(3x)}\frac{2x}{3x}$

12. myininaya

2/3*1*1*2/3=4/9

13. myininaya

got it? do you remember what sinx/x goes to as x goes to 0?