# Limit involving floor function + limit involving fundamental trig limit HELP! :)

• Apr 14th 2013, 11:18 PM
iMagoo
Limit involving floor function + limit involving fundamental trig limit HELP! :)
Hi all!

I have a couple questions I'm struggling with in my University homework, would love some guidance! Not after just the answer, that does not help me learn!

First up is the following limit:

Attachment 27962

I am struggling to understand how I should go about this question, I am aware the answer is -1, but would like some guidance as to how to get onto the right track towards that answer.

Next up is the following limit:

Attachment 27963

I believe I can apply L'Hopital's rule, but the question specifically asks me to write it in the form:

Attachment 27964

where y and z are functions of x, so that the fundamental trig limit can be utilized and A is a real number scalar.
Thus, I am not sure how to express it in that form, so guidance as to what trig identities I should use etc. will be greatly appreciated!

Thanks in advanced for any help!

Cheers
• Apr 15th 2013, 02:30 AM
Plato
Re: Limit involving floor function + limit involving fundamental trig limit HELP! :)
Quote:

Originally Posted by iMagoo
First up is the following limit:
Attachment 27962
Next up is the following limit:
Attachment 27963

For the first one, graph the function near $\displaystyle x=-2$.

You do not need L'Hopital's rule for the second:
$\displaystyle \frac{\sin(2x)}{\sin(5x)}=\frac{2}{5}\frac{\frac{\ sin(2x)}{2x}}{\frac{\sin(5x)}{5x}}$.
• Apr 15th 2013, 08:37 AM
johng
Re: Limit involving floor function + limit involving fundamental trig limit HELP! :)
Hi,
I've attached some remarks on the floor function. I hope it helps.

Attachment 27969
• Apr 16th 2013, 12:36 AM
iMagoo
Re: Limit involving floor function + limit involving fundamental trig limit HELP! :)
Thanks very much for the help guys, much appreciated!