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Math Help - Functions (Limits)

  1. #1
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    Functions (Limits)

    So...

    I'm a little confused as of what I got to do here but this is what I've done so far.

    <br />
f(x)<br />
is given. Find  f(x+\Delta x).

    <br />
f(x) = x^2+1<br />

    <br />
(x+\Delta x)^2 + 1<br />

    <br />
(x+\Delta x)(x+\Delta x)+1<br />

    <br />
= x^2+2x\Delta x+\Delta x^2+1<br />

    So...That it I'm done?
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  2. #2
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    = (1+\Delta) x^2+2x\Delta x+1

    No limit was asked?
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  3. #3
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    nope, no limit asked, just said open up parentheses that why I left it like that
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  4. #4
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    Quote Originally Posted by drkidd22 View Post
    So...

    I'm a little confused as of what I got to do here but this is what I've done so far.

    <br />
f(x)<br />
is given. Find  f(x+\Delta x).

    <br />
f(x) = x^2+1<br />

    <br />
(x+\Delta x)^2 + 1<br />

    <br />
(x+\Delta x)(x+\Delta x)+1<br />

    <br />
= x^2+2x\Delta x+\Delta x^2+1<br />

    So...That it I'm done?
    Are you meant to find the difference quotient?
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  5. #5
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    Just says simplify completly
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  6. #6
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    I'm stuck on this simplifying this one.

    <br />
f(x)=\sqrt{x^2-1}<br />

    <br />
=\sqrt{(x+\Delta x)^2-1}<br />

    <br />
=\sqrt{x^2+2x\Delta x+\Delta x^2-1}<br /> <br />
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  7. #7
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    Quote Originally Posted by drkidd22 View Post
    I'm stuck on this simplifying this one.

    <br />
f(x)=\sqrt{x^2-1}<br />

    <br />
=\sqrt{(x+\Delta x)^2-1}<br />

    <br />
=\sqrt{x^2+2x\Delta x+\Delta x^2-1}<br /> <br />
    you're done.
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