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First Principles-( ε-δ methods) proof.

  1. Dec 14, 2011 #1
    (X^2+1)/(X^3-9) → -1/4 as x → 1

    (without using algebra of limits. Also constructing δ explicitly).

    I have attempted this question but to no avail,

    I start like this:

    = |(X^2+1)/(X^3-9)+1/4|

    = (4(X^2+1)+X^3-9)/ 4(X^3-36)

    try factorisation but am unsuccessful.

    Anybody lend a helping hand?
  2. jcsd
  3. Dec 14, 2011 #2


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    Expand (multiply out) the terms in the numerator. Then collect like terms and factor the result.

    That's a start.
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