## grantmasini 2 years ago Limits

1. grantmasini

$\cos x \lim_{h \rightarrow 0}\frac{ \sin h }{ h }$

2. zzr0ck3r

have you learned lhospital rule ?

3. grantmasini

no.

4. zzr0ck3r

what are you doing in class?

5. zzr0ck3r

squeeze theorem?

6. grantmasini

this is one of the last steps in a limit problem from the first unit (limits). it's supposed to evaluate to cosx*1=cosx. I don't understand how sinh/h comes out to be 1?

7. zzr0ck3r

well, there is a thing called La'Hospital rule, that says when you run a limit and get 0/0 you can take the derivative of the top and the derivative of the bottom and then run the limit again so your limit lim of sin(h)/h = lim of cos(h)/1 = lim cos(h) and at 0 that is 1

8. zzr0ck3r

l'hopital's rule

9. grantmasini

lol, we are on the first unit. haven't learned derivates, or any of the theorems or rules.

10. grantmasini

can someone just explain how the limit of sinh/h is 1?

11. grantmasini

derivatives*

12. zzr0ck3r

hmm

13. zzr0ck3r

do you know the squeeze theorem?

14. zzr0ck3r

There is a geometric proof http://www.youtube.com/watch?v=Ve99biD1KtA I don't know of an elementary way of showing this limit without geometry and quite a bit of explaining...watch that video.

15. grantmasini

all right, thanks

16. zzr0ck3r

np

17. PROSS

It appears that you are beginning the study of Calculus with the topic of limits. We often will use a table of values as they approach the limit from the left and from the right. This is the first method you may want to use. A second method that is used is to look at the graph of the function. You can easily see that the limit as h approaches 0 from the left and right is 1. I hope this helps.