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Math Help - Help. Can I do this? (Delta Epsilon)

  1. #1
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    Help. Can I do this? (Delta Epsilon)

    Hi everyone. I'm a bit stuck on doing this Delta Epsilon prrof for the limit
    lim x->1 \sqrt{x}=1
    I have (I'll use brakets for absolute values)
    ( \sqrt{x}-1)<e and 0<(x-1)<d
    so
    (x-1)< e^s
    so d= e^2 ?????


    ok then i'm stuck and don't know where from here...i'm not even sure if i have done that right

    any help?
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  2. #2
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    Can you show that if |x-1|<1 then  \frac{1}{{\sqrt x  + 1}} < 1?
    If you can then choose \delta  = \min \left\{ {1,\varepsilon } \right\}.
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  3. #3
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    Hi
    If i have f(x)-L < e
    then sqrt(x)-1 < e
    if i then multiply by ( \sqrt{x}+1)
    i get x-1 < e( \sqrt{x}+1)
    is that right?

    but if [x-1] = ( \sqrt{x}-1)( \sqrt{x}+1)

    if i then cancel from both sides i'm back where i started at \sqrt{x}-1<e

    I think i just keep turning back on myself....I'm not being able to get a 'd'
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