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Math Help - Limits,Prove that F(x) > A when x==> a

  1. #1
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    Limits,Prove that F(x) > A when x==> a

    Hello,I need help in proving :
    (Note a is totally different than A )
    If Limit F(x) x==>a = L (equals L ) and A<L then for an 'x' which is very close to a we get that F(x)>A

    Any ideads?

    Thanks
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  2. #2
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    The definition of \lim_{x\to a}F(x)=L starts with "For every \varepsilon>0, ...". Substitute, say, \varepsilon=(L-A)/2 (or any concrete \varepsilon that is less than L-A) and see what the rest of the definition says.
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  3. #3
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    Quote Originally Posted by emakarov View Post
    The definition of \lim_{x\to a}F(x)=L starts with "For every \varepsilon>0, ...". Substitute, say, \varepsilon=(L-A)/2 (or any concrete \varepsilon that is less than L-A) and see what the rest of the definition says.
    Aha I see,but why its not correct to choose L - A? ;

    0<|x-a|<dlta ====> |F(x)- L|< e

    by |y|<m >> -m<y<m

    We get ; -e<F(x)-L<e

    Now e=L -A
    so ==> F(x) - L > -e = -(L -A)=A - L
    / + (-L)
    ===> F(x)>A- L + L = A ==> F(x)> A!

    Not correct ?(it is given that L -A >0,so the value of e is positive! and it fits with the requirements! )

    Thank you
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  4. #4
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    You are right; this works too.
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  5. #5
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    Quote Originally Posted by emakarov View Post
    You are right; this works too.
    Thank you issue been solved!
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