quick question

Well, I guess it depends what level they are at.. I am assuming it is high-school. I would probably just do it like: If we know that lim (sin(theta)/theta)=1 then this means that lim sin(theta)= lim theta for theta=>0 .. since the limit of a product is equal to the product of the limits. ..

so what do we get limit theta^2/ limit theta^2 =1 can you cancel limits like that

well again, the limit of products it the product of limits, so you say:

limit theta^2/ limit theta^2= limit(theta^2/theta^2) = limit(1)=1 ..

But it's been 3.5 years since I had any analysis, so you may wanna check it with some of the other guys here.. =)

lol

ehh its just one problem

thanks for the input

RainbowRising, how is your solution? ..

The pinching theorem?? What is that? The squeeze theorem? Remember it is high-school level.. so I don't assume we have to be too regoristic .. Then you might as well use the l'Hopital if you want to go beyond first-second year high-school stuff..

no i think u do use the squeeze theorem thanks

They know the squeeze theorem, but they don't know Taylor expansion or l'Hopital!? Did I wake up in the right world?

thats how we roll in america...lol

Americans are weird like that...  I still haven't understood why my county makes us do an art project on the Golden Ratio in the Geometry curriculum.

Hi DrKnowNothing,

One can indeed divide by 1 or multiply by an expression that = 1 to obtain the proper limit identity for either sin or cos (these are the two main IDs taught in standard calc books). After doing so, one will get the appropriate limit number times what you pull out in front of the identity that is being multiplied. What you pull out in front relies on what you had to do to mutiply or divide an expression by 1. Then simplify your product.

I am not sure that we can use the Intermediate Value Theorem (because [-1,1] is rather easy to multiply by), but this is another avenue to explore.

strangequark

I realize I have posted late and on the 2nd page! Sorry for redundancy!