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Question about indeterminate form

  1. Dec 20, 2014 #1
    why $$1^\infty$$ is indeterminate form?
     
  2. jcsd
  3. Dec 20, 2014 #2

    Mark44

    Staff: Mentor

    1 raised to any finite power is 1, of course, but some limits are of this indeterminate form, and have a limit that isn't equal to 1.

    The most famous example is this limit:
    $$\lim_{x \to \infty}(1 + \frac{1}{x})^x$$

    The base is approaching 1 and the exponent is "approaching" infinity. It can be shown that the value of this limit expression is the number e.
     
  4. Dec 20, 2014 #3
    Thanks ,, I got it now
    (:
     
  5. Dec 20, 2014 #4

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
     
  6. Dec 21, 2014 #5

    Mentallic

    User Avatar
    Homework Helper

    I don't believe that [itex]1/\infty[/itex] is an indeterminate form because its value cannot be anything other than 0.
     
  7. Dec 21, 2014 #6

    Mark44

    Staff: Mentor

    I agree. It's not indeterminate because you can determine what the limit will be.
     
  8. Dec 21, 2014 #7

    Mark44

    Staff: Mentor

    That's not true. While ##[\infty - \infty]## and ##[\frac{\infty}{\infty}]## are indeterminate forms, ##[\infty + \infty]## and ##[\infty * \infty]## are not considered indeterminate.
     
  9. Dec 22, 2014 #8
    Me too .

    How about
    $$\frac{0}{\infty}$$

    Is it indeterminate too?

    I think so

    :oldeyes:
     
  10. Dec 22, 2014 #9

    Mark44

    Staff: Mentor

    No, it is not indeterminate. If the numerator approaches 0 and the denominator becomes unbounded, the limit is 0.
     
  11. Dec 22, 2014 #10
    Oh, I see,,
    Thanks
     
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