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Math Help - Limits

  1. #1
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    Cool Limits

    How do I find these limits? Please help!

    \lim_{x \to 14}\frac{\sqrt{x+2}-4}{70-19x+x^2}

    \lim_{x \to 13}\frac{-26+2x}{\sqrt{x+3}-4}
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  2. #2
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    Re: Limits

    Quote Originally Posted by Lotte1990 View Post
    How do I find these limits? Please help!

    \lim_{x \to 14}\frac{\sqrt{x+2}-4}{70-19x+x^2}

    \lim_{x \to 13}\frac{-26+2x}{\sqrt{x+3}-4}
    L_1=\displaystyle 	\lim_{x \to 14}\frac {(x-14)}{(x-14)(x-5)(\sqrt{x+2}+4)}=\frac{1}{72}

    L_2=2\cdot \displaystyle \lim_{x \to 13} \frac{(x-13)(\sqrt{x+3}+4)}{(x-13)}=16
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  3. #3
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    Re: Limits

    Can you please explain your calculation? I need some more information... Thanks!
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  4. #4
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    Re: Limits

    For the first one, rationalise the numerator by multiplying top and bottom by the top's conjugate.
    For the second one, rationalise the denominator by multiplying top and bottom by the bottom's conjugate.
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  5. #5
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    Re: Limits

    A useful fact for problems of this sort: if P is a polynomial such that P(a)= 0 then x- a is a factor or P(x).

    Also, if you have a term involving a root that is 0 when x= a, then rationalizing it will give a polynomial with a factor of x- a.
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