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Math Help - Limits

  1. #1
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    Limits

    Can someone please help me? walk me through this?

    lim (1/x) -1/(x^2)+x)
    x->0
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by darkblue View Post
    Can someone please help me? walk me through this?

    lim (1/x) -1/(x^2)+x)
    x->0
    First of all, we should verify our associations.

    Is this what you meant?

    \lim_{x\to0}\left(\frac{1}{x}-\frac{1}{x^2+x}\right)
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  3. #3
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    Quote Originally Posted by VonNemo19 View Post
    First of all, we should verify our associations.

    Is this what you meant?

    \lim_{x\to0}\left(\frac{1}{x}-\frac{1}{x^2+x}\right)
    yes that exactly
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by darkblue View Post
    yes that exactly
    Begin by combining the fractions by finding the LCD and note the indeterminate form \frac{0}{0}.

    Do you know how to proceed?
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  5. #5
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    Quote Originally Posted by VonNemo19 View Post
    Begin by combining the fractions by finding the LCD and note the indeterminate form \frac{0}{0}.

    Do you know how to proceed?
    ok so i got (x^2)-2x all over (x^3)-(x^2)

    now i really dont know what to do....
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  6. #6
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    use l'hospital's rule. I advise you to look it up in your textbook or google it.
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  7. #7
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by darkblue View Post
    ok so i got (x^2)-2x all over (x^3)-(x^2)

    now i really dont know what to do....
    That's not quite right.

    First note that \frac{1}{x}-\frac{1}{x^2+x}=\frac{1}{x}-\frac{1}{x(x+1)}.

    The LCD is x(x+1). Can you try to combine the fractions now? You should see some kind of nice cancellation occur.


    Quote Originally Posted by superdude View Post
    use l'hospital's rule. I advise you to look it up in your textbook or google it.
    L'H˘pital's rule is overkill for this one.
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  8. #8
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    Quote Originally Posted by darkblue View Post
    ok so i got (x^2)-2x all over (x^3)-(x^2)

    now i really dont know what to do....
    forget how to combine fractions?

    \frac{1}{x} - \frac{1}{x^2+x}

    \frac{1}{x} - \frac{1}{x(x+1)}

    \frac{x+1}{x(x+1)} - \frac{1}{x(x+1)}

    \frac{(x+1) - 1}{x(x+1)}

    \frac{x}{x(x+1)}
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  9. #9
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    Quote Originally Posted by skeeter View Post
    forget how to combine fractions?

    \frac{1}{x} - \frac{1}{x^2+x}

    \frac{1}{x} - \frac{1}{x(x+1)}

    \frac{x+1}{x(x+1)} - \frac{1}{x(x+1)}

    \frac{(x+1) - 1}{x(x+1)}

    \frac{x}{x(x+1)}

    okay thankyou. but now after doing that and we are left with
    \frac{x}{x(x+1)} what do i do now?
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  10. #10
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by darkblue View Post
    okay thankyou. but now after doing that and we are left with
    \frac{x}{x(x+1)} what do i do now?
    Cancel the x's and substitute directly.
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  11. #11
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    Quote Originally Posted by VonNemo19 View Post
    Cancel the x's and substitute directly.
    ok thank you..so i get 1/(x+1) substitute zero and get 1/1 = 1

    so is the limit 1 then?
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  12. #12
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by darkblue View Post
    ok thank you..so i get 1/(x+1) substitute zero and get 1/1 = 1

    so is the limit 1 then?
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