## hba 4 years ago Limit Question.

1. hba

$\lim_{x \rightarrow 0}\frac{ \sin2x }{ \sin3x }$

2. anonymous

2/3

3. hba

4. anonymous

ok

5. anonymous

one min

6. anonymous

since you have indeterminate form, you have to use L'hospital rule

7. anonymous

then when you do derivative you get $\frac{ 2\cos2x }{ 3\cos3x }$

8. hba

I dont know l hospitals rule.

9. anonymous

you don't?

10. anonymous

you know like squeeze theorem?

11. hba

Please teach me how to solve it,i am helpless :(

12. anonymous

oki so there are couple cases when you have indeterminate form, for example 0/0 , inf/inf

13. anonymous

so what you do then is basically take the derivative of the top and the bottom

14. anonymous

for example $\lim_{x \rightarrow 1} \frac{ x^3+x^2=2x }{ x-1 }$

15. anonymous

it suppose to be x^3+x^2-2x

16. anonymous

so if you plug 1 in you get 0/0 which is indeterminate as it has no meaning. so you have to apply l'hospital, derivative of the top and bottom