Question

Limits

Answer 1

\[\cos x \lim_{h \rightarrow 0}\frac{ \sin h }{ h }\]

Answer 2

have you learned lhospital rule ?

Answer 3

no.

Answer 4

what are you doing in class?

Answer 5

squeeze theorem?

Answer 6

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?

Answer 7

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

Answer 8

l'hopital's rule

Answer 9

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

Answer 10

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

Answer 11

derivatives*

Answer 12

hmm

Answer 13

do you know the squeeze theorem?

Answer 14

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.

Answer 15

all right, thanks

Answer 16

np

Answer 17

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.