1. ## The Sandwich Theorem

Used To Be Able To Find The Limit And Confirm It. I Really Don't Know How To Use The Sandwich Theorem.

I just don't understand how and when to use it, for example:

lim x-> infinity (1-cosx) / x^2

in the book, it gives and example ofsinx / x which i get up to some point, and then i lose myself :/

2. Originally Posted by >_<SHY_GUY>_<
Used To Be Able To Find The Limit And Confirm It. I Really Don't Know How To Use The Sandwich Theorem.

I just don't understand how and when to use it, for example:

lim x-> infinity (1-cosx) / x^2

in the book, it gives and example ofsinx / x which i get up to some point, and then i lose myself :/

The Largest possible value of cos(x) is 1 so the smallest possible value of 1- cos x is 0. The smallest possible value of cos(x) is -1 so the largest possible value of 1- cos x is 2: [tex]0\le 1- cos x\le 2[/itex]. That means (dividing through be $\displaystyle x^2$ that $\displaystyle 0\le \frac{1- cos x}{x^2}\le \frac{2}{x^2}$ because both 0 and $\displaystyle \frac{2}{x^2}$ go to 0, and $\displaystyle \frac{1- cos}{x^2}$ is "sandwiched between them", it must also go to 0.

3. Originally Posted by HallsofIvy
The Largest possible value of cos(x) is 1 so the smallest possible value of 1- cos x is 0. The smallest possible value of cos(x) is -1 so the largest possible value of 1- cos x is 2: [tex]0\le 1- cos x\le 2[/itex]. That means (dividing through be $\displaystyle x^2$ that $\displaystyle 0\le \frac{1- cos x}{x^2}\le \frac{2}{x^2}$ because both 0 and $\displaystyle \frac{2}{x^2}$ go to 0, and $\displaystyle \frac{1- cos}{x^2}$ is "sandwiched between them", it must also go to 0.
following that equation, how can you tell that the limit is 0? [im sorry if you had alredy answered that, it confusing somewhat].
and how can you use the sandwich theorem for any other equation? does it follow any steps?

4. Hi

i had the same problem, until i watch this on you tube.

The person explains clearly what the sandwhich Theorem (or the Squeeze Theorem which the person calls it) is.