What Is the Limit of cos(1/(10-t)) as t Approaches 10?

[Jan Hill]

Homework Statement

limit as t-->10 of cos (1/10-t)

Homework Equations

The Attempt at a Solution

Obviously we can't substitute in t = 10 or it would be undefined, so how do we do this. Is there an inequalitly that I haven't considered?

 

[PhMichael]

supposing that the function is: cos(\frac{1}{10-t})
well, the limit does not exist because the cosine function will oscillate crazily between 1 and -1 as t->10.

 

[Jan Hill]

Thanks. I was looking at

lim t-->10 of (t^2-100)/t times cos1/(10-t) + 100

So since the lim as t-->10 of cos1/(10 - t) is undefined, we're left with 100


By the way, I'd use the proper way of expressing math information with symbols etc. if I knew how to use it but I don't know where to get the symbols etc. to be able to use them. Do you know how to remedy this issue?

 

[Mentallic]

Yes that's right, but with a little change of words - it's not because it's "undefined" but because the limit doesn't exist and it's because of this oscillation between -1 and 1 that we can conclude it is finite as the limit approaches, thus the limit is 0 due to the other factor.

It's called Latex and the way you use it is by using the tags [ tex ] ...code... [ /tex ] (without the spaces in the tex tags). You can find some code to use by searching through the Sum symbol in the full text editor when you type out your message.

 

[Jan Hill]

thank you very much

 

[Jan Hill]

Do I need to download Latex to my pc? I have looked at it and I see how great it will be but how do I get to use it!?

 

[Mentallic]

No you just type it into your message. To get an idea of how to use it, click on the latex I'm going to do to show you how you would do a fraction.

\frac{1}{2}

 

[M Dhanota]

Is there any way that we would be able to simplify any parts of the equation and then take the limit? Or its just a substitution problem?

 

[Mentallic]

Not really, but if you prefer a limit going to zero rather than 10, let u=t-10

Then you have,

\lim_{u\to 0}\frac{u(u+20)}{u+10}cos\left(\frac{-1}{u}\right)+100

 

[Mark44]

By the way, I'd use the proper way of expressing math information with symbols etc. if I knew how to use it but I don't know where to get the symbols etc. to be able to use them. Do you know how to remedy this issue?

Here are some links to sites that show how to use LaTeX.
http://heather.cs.ucdavis.edu/~matloff/LaTeX/LookHereFirst.html
http://andy-roberts.net/misc/latex/latextutorial9.html
http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Commands

There are a lot of things you can do without using LaTeX, such as exponents and subscripts. To get the extended menu (appears above the text input window), click Go Advanced below the text input window. Use the X² button to write exponents and use the X₂ to write subscripts.

 

[M Dhanota]

Thanks Mentallic! :)

 

[Mentallic]

No problem!