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Math Help - Limits that exist and dont

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    Post Limits that exist and dont

    Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
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    Quote Originally Posted by Newskin01 View Post
    Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
    A limit doesn't have to be continuous at a point to exist. The LHS and RHS limits need to be equal for the limit to exist.
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    Quote Originally Posted by Newskin01 View Post
    Why can a limit be 0/0 and still exist, but what is the reason it exists?
    Because, limits are about what happens to a function near a point.
    We never consider the value at the point.
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    Quote Originally Posted by Newskin01 View Post
    Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
    an existent limit that yields the indeterminate form 0/0 upon direct substitution has a "hole" (a point discontinuity) at the limit value.

    however, not all limits with the 0/0 indeterminate form exist ...

    \displaystyle \lim_{x \to 0} \frac{|x|}{x}
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  5. #5
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    Quote Originally Posted by Newskin01 View Post
    Why can a limit be 0/0 and still exist. I know that you can simplify it, but what is the reason it exists?
    Remember that 0/0 can mean any number (0x = 0) or no number. The type of equation will put an implicit constraint specifying the number if the limit exists (e.g. the limit as x approaches 0 for sinx/x)
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