Limits & Squeeze Theorem for limit of f(x) = x^2 sin(1/x)

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"Consider the graph of the function f(x)=x[sup:15ti0g72]2[/sup:15ti0g72]sin(1/x). Show how you can use the Squeeze Theorem to prove that the lim (x-> 0) f(x)=0.

By finding two simple functions h(x) and g(x) which trap the value of f(x) between them. Of course, you will need to choose these functions so you are SURE they have the appropriate limits at x=o as well."

I have no idea what to do or where to start. Any help or direction would be greatly appreciated.

 

[Deleted member 4993]

Re: Limits & Squeeze Theorem

"Consider the graph of the function f(x)=x[sup:224jfkvw]2[/sup:224jfkvw]sin(1/x). Show how you can use the Squeeze Theorem to prove that the lim (x-> 0) f(x)=0.

By finding two simple functions h(x) and g(x) which trap the value of f(x) between them. Of course, you will need to choose these functions so you are SURE they have the appropriate limits at x=o as well."

I have no idea what to do or where to start.

Does that mean - you do not know what squeeze theorem is??

What does your textbook say - what does your class-notes say??

Any help or direction would be greatly appreciated.

If your text book is no help - then do a google search on squeeze theorem.

In particular, go to:

http://www.math.ucdavis.edu/~kouba/Calc ... ciple.html

to see some examples.

 

[heartshapes]

Re: Limits & Squeeze Theorem

My teacher just gave us the problems without any direction at all.

Thanks. What should I make h(x) and g(x)?

 

[heartshapes]

Re: Limits & Squeeze Theorem

Nevermind. Thanks!

 

[Pklarreich]

Re: Limits & Squeeze Theorem

"Consider the graph of the function f(x)=x[sup:2pqxsl6i]2[/sup:2pqxsl6i]sin(1/x). Show how you can use the Squeeze Theorem to prove that the lim (x-> 0) f(x)=0.

By finding two simple functions h(x) and g(x) which trap the value of f(x) between them. Of course, you will need to choose these functions so you are SURE they have the appropriate limits at x=o as well."

I have no idea what to do or where to start. Any help or direction would be greatly appreciated.

How about using this fact:

Since -1 <= sin (1/x) <= 1

-x^2 <= x^2 sin (1/x) <= x^2

That should do it.