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Why eliminate answers?

  1. May 31, 2008 #1
    [SOLVED] Why eliminate answers?

    In my book, Essential Calculus, a section is introduced with limits. They introduce a random(maybe) function :

    [tex]Q(h) = \frac {2h + h^2}{h} (h \neq 0)[/tex]

    "We then divide the numerator by the denominator h, which is permissible since [tex]h \neq 0[/tex]. This gives the simple formula [tex]Q(h) = 2 + h (h \neq 0)[/tex]"

    I was always told you do not divide by variables like in a trigonometric equation because it eliminates solutions. How are they then to say that it is permissible since [tex]h \neq 0[/tex] ? I don't understand.
  2. jcsd
  3. May 31, 2008 #2
    In this case, it is fine. Given that [tex]h \neq 0[/tex], both functions are equal because you are only simplifying the function.
  4. May 31, 2008 #3


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    Hi razored! :smile:

    It's ok because all these calculus equations begin "lim as h -> 0".

    So it's impossible for h to be 0. :smile:

    (oh … and look up L'Hôpital's Rule :wink:)
  5. Jun 1, 2008 #4


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    What "solutions" do you mean? You are not "solving" an equation here.
  6. Jun 1, 2008 #5
    Whoops. That is what I misunderstood. Thanks for pointing that out!
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