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Math Help - Limit involving floor function + limit involving fundamental trig limit HELP! :)

  1. #1
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    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:

    Limit involving floor function + limit involving fundamental trig limit HELP! :)-lim.jpg

    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:

    Limit involving floor function + limit involving fundamental trig limit HELP! :)-lim2.jpg

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

    Limit involving floor function + limit involving fundamental trig limit HELP! :)-lim3.jpg

    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
    Last edited by iMagoo; April 15th 2013 at 12:05 AM.
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  2. #2
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    Re: Limit involving floor function + limit involving fundamental trig limit HELP! :)

    Quote Originally Posted by iMagoo View Post
    First up is the following limit:
    Click image for larger version. 

Name:	lim.jpg 
Views:	2 
Size:	3.5 KB 
ID:	27962
    Next up is the following limit:
    Click image for larger version. 

Name:	lim2.jpg 
Views:	16 
Size:	3.5 KB 
ID:	27963

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

    You do not need L'Hopital's rule for the second:
    \frac{\sin(2x)}{\sin(5x)}=\frac{2}{5}\frac{\frac{\  sin(2x)}{2x}}{\frac{\sin(5x)}{5x}}.
    Thanks from iMagoo
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  3. #3
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    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.

    Limit involving floor function + limit involving fundamental trig limit HELP! :)-mhffloorceil.png
    Thanks from iMagoo
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  4. #4
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    Re: Limit involving floor function + limit involving fundamental trig limit HELP! :)

    Thanks very much for the help guys, much appreciated!
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