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Math Help - Two variable limit question (Question/Solution/Answer included)

  1. #1
    s3a
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    Two variable limit question (Question/Solution/Answer included)

    I get how to find the limit by plugging in x = 0, evaluating what the limit is and and then taking y = 0 and evaluating what the limit is and if each limit is the same then the limit does exist and is that number. (Tell me if I am wrong in thinking this).

    Using the methodology described above, I get the correct answer but the problem attached shows me a solution that I do not understand and would really appreciate it if someone could explain to it to me.

    Basically, I would like to know if my way is correct and whether it is or not, I would like to understand this different way as well.

    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Two variable limit question (Question/Solution/Answer included)-q3.jpg  
    Last edited by s3a; November 7th 2011 at 02:34 PM.
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  2. #2
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    Re: Two variable limit question (Question/Solution/Answer included)

    Quote Originally Posted by s3a View Post
    I get how to find the limit by plugging in x = 0, evaluating what the limit is and and then taking y = 0 and evaluating what the limit is and if each limit is the same then the limit does exist and is that number. (Tell me if I am wrong in thinking this).
    Using the methodology described above, I get the correct answer but the problem attached shows me a solution that I do not understand and would really appreciate it if someone could explain to it to me.
    Basically, I would like to know if my way is correct and whether it is or not, I would like to understand this different way as well.!
    There is a brief answer: NO, not correct.
    Why not post an exact question so that we can explain?
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  3. #3
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    Re: Two variable limit question (Question/Solution/Answer included)

    Nothing is attached.

    If the two limits you describe are the same, then you have proved nothing. If they are different, then you have shown that the limit does not exist.
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  4. #4
    s3a
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    Re: Two variable limit question (Question/Solution/Answer included)

    Thank you both but especially SammyS that explanation was important to me and helps me realize that me getting the answer was just by coincidence and more.

    I'm attaching the image now in the initial post.
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    Re: Two variable limit question (Question/Solution/Answer included)

    Quote Originally Posted by s3a View Post
    I'm attaching the image now in the initial post.
    Now that we can see your image, the limit is 0.
    Note that x=r\cos(\theta),~y=r\sin(\theta)~\&~x^2+y^2=r^2 .

    If you make those substitutions the limit is clear.
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