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Math Help - More Difference Quotient

  1. #1
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    More Difference Quotient

    Find the difference quotient for the given function.

    y = x + (1/x)
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Find the difference quotient for the given function.

    y = x + (1/x)
    let f(x) = x+\dfrac{1}{x}. Now just plug in the following equation:

    Difference quotient: \dfrac{f(x+h) - f(x)}{h}
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  3. #3
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    no........

    Quote Originally Posted by Pn0yS0ld13r View Post
    let f(x) = x+\dfrac{1}{x}. Now just plug in the following equation:

    Difference quotient: \dfrac{f(x+h) - f(x)}{h}
    I'm sorry but reaching the answer involves more than what you suggested.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    Find the difference quotient for the given function.

    y = x + (1/x)
    Using the definition of the difference quotient, we have \frac{x+h+\displaystyle\frac{1}{x+h}-\left[x+\displaystyle\frac{1}{x}\right]}{h}=\frac{h+\displaystyle\frac{1}{x+h}-\frac{1}{x}}{h}

    The goal here is to get the h term in the denominator to disappear.

    First, we need to combine the terms in the numerator.

    The common denominator is x(x+h)

    Thus, the difference quotient becomes \frac{\displaystyle\frac{hx(x+h)}{x(x+h)}+\frac{x}  {x(x+h)}-\frac{x+h}{x(x+h)}}{h}=\frac{\displaystyle\frac{hx  ^2+h^2x-h}{x(x+h)}}{h}=\frac{h\left(x^2+hx-1\right)}{h\left[x(x+h)\right]} =\color{red}\boxed{\frac{x^2+hx-1}{x(x+h)}}

    Does this make sense?

    By the way, to add on to what I told you in the other thread, when simplifying the difference quotient, the objective is to get the h term in the denominator to disappear (i.e. cancel out with something in the numerator of the difference quotient).
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  5. #5
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    a lot...

    Quote Originally Posted by Chris L T521 View Post
    Using the definition of the difference quotient, we have \frac{x+h+\displaystyle\frac{1}{x+h}-\left[x+\displaystyle\frac{1}{x}\right]}{h}=\frac{h+\displaystyle\frac{1}{x+h}-\frac{1}{x}}{h}

    The goal here is to get the h term in the denominator to disappear.

    First, we need to combine the terms in the numerator.

    The common denominator is x(x+h)

    Thus, the difference quotient becomes \frac{\displaystyle\frac{hx(x+h)}{x(x+h)}+\frac{x}  {x(x+h)}-\frac{x+h}{x(x+h)}}{h}=\frac{\displaystyle\frac{hx  ^2+h^2x-h}{x(x+h)}}{h}=\frac{h\left(x^2+hx-1\right)}{h\left[x(x+h)\right]} =\color{red}\boxed{\frac{x^2+hx-1}{x(x+h)}}

    Does this make sense?

    By the way, to add on to what I told you in the other thread, when simplifying the difference quotient, the objective is to get the h term in the denominator to disappear (i.e. cancel out with something in the numerator of the difference quotient).
    That's a lot of math, mate.
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