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Math Help - Very basic limit help required!

  1. #1
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    Very basic limit help required!

    Ok, so i was learning about limits and came across this questions

    Find:

    Lim
    h-->0

    4x^2 X h^2 + xh + h
    / (divided by)
    h

    So I cancelled it down to 4x^2h + x

    Then I made h = 0 and that got rid of the 4x^2h and left the x

    so the answer I got was x

    but the book says the answer is x + 1

    did I make an error? Can anyone offer assistance?

    Thanks a lot... PS I'm new here so hi all
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  2. #2
    MHF Contributor
    Joined
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    Talking

    Quote Originally Posted by calculusstruggler View Post
    Ok, so i was learning about limits and came across this questions

    \mbox{Find }\, \lim_{h\rightarrow 0}\, \frac{4x^2 h^2\, +\, xh\, +\, h}{h}

    So I cancelled it down to 4x^2h + x
    Um... no....

    You can only cancel factors, not terms or parts of terms. To learn how to simplify rational expressions, try here.

    Then I made h = 0 and that got rid of the 4x^2h and left the x

    Try using one of the techniques they showed you in your book and / or in your classroom lecture: noting that the numerator does not factor, instead divide everything by h:

    . . . . . \left(\frac{4x^2 h^2\, +\, xh\, +\, h}{h}\right)\left(\frac{\frac{1}{h}}{\frac{1}{h}}\  right)

    . . . . . \frac{\frac{4x^2 h^2}{h}\, +\, \frac{xh}{h}\, +\, \frac{h}{h}}{\frac{h}{h}}

    . . . . . \frac{4x^2 h\, +\, x\, +\, 1}{1}

    . . . . . 4x^2 h\, +\, x\, +\, 1

    Now there is no "division by zero" problem, so you can simply evaluate at h = 0, thus confirming the book's answer.
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  3. #3
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    Quote Originally Posted by calculusstruggler View Post
    Ok, so i was learning about limits and came across this questions

    Find:

    Lim
    h-->0

    4x^2 X h^2 + xh + h
    / (divided by)
    h

    So I cancelled it down to 4x^2h + x

    Then I made h = 0 and that got rid of the 4x^2h and left the x

    so the answer I got was x

    but the book says the answer is x + 1

    did I make an error? Can anyone offer assistance?

    Thanks a lot... PS I'm new here so hi all
    shouldnt you get 4hx^2 + x + 1?? then setting h to zero would give you x+1

     \tfrac {4x^2h^2 + xh + h}{h} = \tfrac {4x^2h^2}{h} + \tfrac {xh}{h} + \tfrac {h}{h} = 4hx^2 + x + 1
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  4. #4
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    ahh thanks guys, I see what I did wrong. I simply cancelled out the h when I divided it by h, but should have made it 1 because h/h = 1 not 0

    Thanks a lot for clearing that up.
    Stupid stupid error, can't make those in the exam!
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