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Math Help - First Principles- Calculus

  1. #1
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    First Principles- Calculus

    Hello math guys, I need desperate help with this first principles problem:

    2/sqrt(x-3)

    showing how to work through this problem would be great to help me get better at these.

    thanks!
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  2. #2
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    Quote Originally Posted by zachattack View Post
    Hello math guys, I need desperate help with this first principles problem:

    2/sqrt(x-3)

    showing how to work through this problem would be great to help me get better at these.

    thanks!
    f(x) = \frac{2}{\sqrt{x-3}}

    f(x+h) = \frac{2}{\sqrt{x+h -3}}

    \lim_{h \to 0} \, \frac{1}{h}\left(\frac{2}{\sqrt{x+h -3}} - \frac{2}{\sqrt{x-3}}\right)

    \lim_{h \to 0} \, \frac{2}{h}\left(\frac{\sqrt{x-3} - \sqrt{x+h-3}}{\sqrt{x-3} \cdot \sqrt{x+h -3}}\right)

    \lim_{h \to 0} \, \frac{2}{h}\left(\frac{\sqrt{x-3} - \sqrt{x+h-3}}{\sqrt{x-3} \cdot \sqrt{x+h -3}}\right) \cdot \frac{\sqrt{x-3} + \sqrt{x+h-3}}{\sqrt{x-3} + \sqrt{x+h-3}}

    \lim_{h \to 0} \, \frac{2}{h}\left(\frac{(x-3) - (x+h-3)}{(x-3)\sqrt{x+h -3}+\sqrt{x-3}(x+h-3)}\right)

    \lim_{h \to 0} \, \frac{2}{h}\left(\frac{-h}{(x-3)\sqrt{x+h -3}+\sqrt{x-3}(x+h-3)}\right)

    \lim_{h \to 0} \, -\frac{2}{(x-3)\sqrt{x+h -3}+\sqrt{x-3}(x+h-3)} = -\frac{2}{2(\sqrt{x-3})^3} = -\frac{1}{(x-3)^{\frac{3}{2}}}

    ... going to bed.
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  3. #3
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    Thanks

    thank you, but can someone please explain how you get 1/h factored out of the rest of the function, I understand the factoring out of the two though
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  4. #4
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    \frac{f(x+h) - f(x)}{h} = \frac{1}{h}[f(x+h) - f(x)]
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  5. #5
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    He applied the formula:

    \frac{f(x + h) - f(x)}{h}

    Beat me to it skeets Go to bed already .
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  6. #6
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    thanks
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