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Math Help - function proof

  1. #1
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    function proof

    (2) Show that lim_{x \to x_0} f(x) = L if and only if lim_{x \to 0} f(x+x_0) = L. Assume x_0 and L are finite.
    (3) Show that if lim_{x \to x_0} f(x) = L and E is a set which has x_0 as an accumulation point, then lim_{x \to x_0, x in E} f(x) = L. Give an example to show that the converse may fail. Assume x_0 and L are finite.

    can anyone solve any of these?
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  2. #2
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    You know that if you could post using even basic LaTeX, we could understand what you are asking. It is very hard to know what you are asking.
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  3. #3
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    what do u mean basic latex?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Here is what you asked in basic LaTex. Incidentally, what you typed was very close to LaTex code, add a few "\"'s and put math tags around it and you would have:

    Quote Originally Posted by ruprotein View Post
    (2) Show that  \lim_{x \to x_0} f(x) = L  if and only if  \lim_{x \to 0} f(x+x_0) = L. Assume x_0 and L are finite.

    (3) Show that if \lim_{x \to x_0} f(x) = L and E is a set which has x_0 as an accumulation point, then \lim_{x \to x_0} f(x) = L, x \in E. Give an example to show that the converse may fail. Assume x_0 and L are finite.

    can anyone solve any of these?
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  5. #5
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    Quote Originally Posted by ruprotein View Post
    (2) Show that lim_{x \to x_0} f(x) = L if and only if lim_{x \to 0} f(x+x_0) = L. Assume x_0 and L are finite.
    \lim_{x\to x_0} f(x) = L means:
    0<|y-x_0| < \delta \implies |f(x) - L| < \epsilon.
    Now if y = x_0+x where 0<|x|<\delta we have:
    |y-x_0| = |x_0+x - x_0| = |x| \in \left( 0, \delta \right)
    Thus,
    |f(x+x_0) - L| < \epsilon.
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  6. #6
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    thanks a lot has anyone ghot the other one?

    Show if lim f(x) = L then if E is any set which has x_o as an accumulation point , lim f(x) = L. But show converse fails.
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  7. #7
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    Quote Originally Posted by ruprotein View Post
    thanks a lot has anyone ghot the other one?

    Show if lim f(x) = L then if E is any set which has x_o as an accumulation point , lim f(x) = L. But show converse fails.
    Is E = \{ f(x) \}?
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  8. #8
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    the guy above restated the question in Latex form
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