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Which Limit Law should I refer to in my solution?

  1. Aug 19, 2011 #1
    1. The problem statement, all variables and given/known data
    Evaluate the limit below indicating the appropriate Limit Law(s) implemented.
    [tex]\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}[/itex]

    2. The attempt at a solution

    [tex]\lim_{x\rightarrow 0.5}\frac{2x^2+5x-3}{6x^2-7x+2}=\lim_{x\rightarrow 0.5}\frac{2(x-0.5)(x+3)}{6(x-0.5)(x-(2/3))}=\lim_{x\rightarrow 0.5}\frac{2(x+3)}{6(x-(2/3))}=-7[/itex]

    So would I be required to state anything when I can out the (x-0.5) factor?
    (PS, I'm doing Real Analysis and have learnt about proving limits from first principles but I'm now trying to learn about using shortcuts by referencing theorems.)
  2. jcsd
  3. Aug 20, 2011 #2


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    Homework Helper

    Did you mean so? Do not mix tex and itex.

    Say that x--->0.5 means that x tends to 0.5 but never equals to it, so x-0.5 can not equal to zero so you can divide with it. After that explain that the limit of a sum is the sum of the limits, limit of a product with a constant is also equal to the constant times the limit, and the limit of the fraction is equal to the limit of the numerator divided by the (non-zero) limit of the denominator .

  4. Aug 20, 2011 #3
    Thank you very much for helping me and fixing up my latex skills. Your explanation about canceling sounds good to me and the other notes about the algebra of limits.
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