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Math Help - finding the tangent line

  1. #1
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    finding the tangent line

    im trying to find the equation of the tangent line at x=8 for y=sqrt(x+1)

    <br />
\lim_{x \to 8}<br />
\frac<br />
{sqrt(x+1)-sqrt(8+1)}{x-8}<br />

    sorry idk the syntax'

    I've gotten this far but i dont know how to get rid of the denominator
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  2. #2
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    Quote Originally Posted by chaosrxn View Post
    im trying to find the equation of the tangent line at x=8 for y=sqrt(x+1)

    <br />
\lim_{x \to 8}<br />
\frac<br />
{\sqrt{(x+1)}-\sqrt{(8+1)}}{x-8}<br />

    sorry idk the syntax'

    I've gotten this far but i dont know how to get rid of the denominator
    Multiply the quotient by 1 = \dfrac{\sqrt{(x+1)}+\sqrt{(8+1)}}{\sqrt{(x+1)}+\sq  rt{(8+1)}} = \dfrac{\sqrt{(x+1)}+3}{\sqrt{(x+1)}+3}

    \lim_{x\to 8}\left(\frac{(\sqrt{x+1}-3)(\sqrt{(x+1)}+3)} {(x-8)(\sqrt{(x+1)}+3)}  \right) = \lim_{x\to 8}\left(\frac{(x-8)} {(x-8)(\sqrt{(x+1)}+3)}  \right)

    Simplify!
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