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Math Help - definition of derivative question

  1. #1
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    Smile definition of derivative question

    Hey getting stuck on this one

    Use definition of the derivative to determine f'(x) where f(x)= \sqrt{3x}

    \lim_{h\rightarrow 0} \frac{f(x+h) - f(x)}{h}

    \lim_{h\rightarrow 0} \frac{\sqrt{3x+3h}-\sqrt{3h}}{h}

    what do i do now?

    thanks
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  2. #2
    Ted
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    Quote Originally Posted by smplease View Post
    Hey getting stuck on this one

    Use definition of the derivative to determine f'(x) where f(x)= \sqrt{3x}

    \lim_{h\rightarrow 0} \frac{f(x+h) - f(x)}{h}

    \lim_{h\rightarrow 0} \frac{\sqrt{3x+3h}-{\color{red} \sqrt{3h}}}{h}

    what do i do now?

    thanks
    the red should be \sqrt{3x}

    to find the limit,start by multiplying by \frac{\sqrt{3x+3h}+\sqrt{3x}}{\sqrt{3x+3h}+\sqrt{3  x}}
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  3. #3
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    So I got it out to this.
    Is this correct?
    Thanks

    <br /> <br />
\lim_{h\rightarrow 0} \frac{\sqrt{3x+3h}-\sqrt{3h}}{h}* \frac{\sqrt{3x+3h}+\sqrt{3x}}{\sqrt{3x+3h}+\sqrt{3  x}}<br /> <br />

    \lim_{h\rightarrow 0} 3*\frac{1}{\sqrt{3x+3h}+\sqrt{3x}}

    (h\neq 0) \frac{3}{\sqrt{3x+0}+\sqrt{3x}}

    = \frac{3}{2\sqrt{3x}}
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  4. #4
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    Quote Originally Posted by smplease View Post
    So I got it out to this.
    Is this correct?
    Thanks

    <br /> <br />
\lim_{h\rightarrow 0} \frac{\sqrt{3x+3h}-\sqrt{3h}}{h}* \frac{\sqrt{3x+3h}+\sqrt{3x}}{\sqrt{3x+3h}+\sqrt{3  x}}<br /> <br />
    Typographical error- this should be
    <br /> <br />
\lim_{h\rightarrow 0} \frac{\sqrt{3x+3h}-\sqrt{3x}}{h}* \frac{\sqrt{3x+3h}+\sqrt{3x}}{\sqrt{3x+3h}+\sqrt{3  x}}<br /> <br />


    \lim_{h\rightarrow 0} 3*\frac{1}{\sqrt{3x+3h}+\sqrt{3x}}

    (h\neq 0) \frac{3}{\sqrt{3x+0}+\sqrt{3x}}

    = \frac{3}{2\sqrt{3x}}
    Yes, that is exactly right!
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