quick question

evaluate 

(all the limits are approaching 0  couldnt get the zeros to show for some reason)

I know this is proly really easy but can some one help me out I am tutoring this girl in calc and have forgotten how to do this!! and she is paying me $25 an hour. I am meeting her in like 8 hours if some one can tell me the trick I would appreciate it :D

Can't you just use l'Hopital? .. Differentiate the top and the bottom independently, by this you get (sin(x)/1) .. then you insert the limit .. by which you get 0/1 = 0 ..

hmm.. totally different story, now that you have changed the whole expression!!

Well, and then again.. probably the same story, just for the new expression, where you may have to use the rule twice..

Aren't all the equations the same?

Oh, it changed!

Maybe you should write it out in normal text.. it seems that the other thing isn't working..

wtf

ok now its right but we are supposed to use the fact that the limit of theta approaching 0 of sin(theta)/theta=1 or that the limit of theta approaching 0 of (1-cos(theta))/theta =0

no l'Hopital allowed

well, by taylor expansion sin(x)=x for x<<1 so there you have it ...

since sin^2(x)=sin(x)*sin(x) .. u get sin(x)*sin(x)=x^2 for x<<1 .. Right!? ..

we are supposed to use this not talyor expansion I think, isnt there a trick using trig identies and basic liimit laws

they havn't learned taylor expansion so that can not be it

Well since they are told that "sin(theta)/theta=1" for theta approaching 0, I guess they can rearrange it to be sin(theta)=theta for theta approaching 0 .. no need to talk about taylor approx. or anything =) ..

that could be it :) thanks

You're welcome =) .. I am reading some nasty center manifold reduction right now, so it is nice to wrap your brain around something you can figure out #)

are you sure that is a valid step that allows you to solve can you show with steps and answer