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Math Help - Determine the value of b?

  1. #1
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    Determine the value of b?

    How do I determine the value of b so that each limit exists?

    \lim_{x \to b} <br />
\frac{4x^2 + 11x -3}{x-b}<br />
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    First you should factor the numerator:

    \lim_{x \to b} \frac{4x^2+11x-3}{x-b} = \lim_{x \to b} \frac{(4x-1)(x+3)}{x-b}

    Now, we should recognize that one of two things can happen from the term in the denominator. There will either be a removable discontinuity or an infinite discontinuity. If the denominator term will cancel with a term in the numerator, that means it will be a removable discontinuity. Otherwise it will be infinite.

    Notice that at a removable discontinuity, the limit exists, but it doesn't exist at an infinite discontinuity.

    So there are two values of b that will cause there to be a removable discontinuity.
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