Question about indeterminate form

  • #1
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Main Question or Discussion Point

why $$1^\infty$$ is indeterminate form?
 

Answers and Replies

  • #2
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why $$1^\infty$$ is indeterminate form?
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.
 
  • #3
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Thanks ,, I got it now
(:
 
  • #4
PeroK
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why $$1^\infty$$ is indeterminate form?
Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
 
  • #5
Mentallic
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Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
I don't believe that [itex]1/\infty[/itex] is an indeterminate form because its value cannot be anything other than 0.
 
  • #6
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I don't believe that [itex]1/\infty[/itex] is an indeterminate form because its value cannot be anything other than 0.
I agree. It's not indeterminate because you can determine what the limit will be.
 
  • #7
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Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
That's not true. While ##[\infty - \infty]## and ##[\frac{\infty}{\infty}]## are indeterminate forms, ##[\infty + \infty]## and ##[\infty * \infty]## are not considered indeterminate.
 
  • #8
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That's not true. While ##[\infty - \infty]## and ##[\frac{\infty}{\infty}]## are indeterminate forms, ##[\infty + \infty]## and ##[\infty * \infty]## are not considered indeterminate.
I agree. It's not indeterminate because you can determine what the limit will be.
Me too .

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

Is it indeterminate too?

I think so

:oldeyes:
 
  • #9
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Me too .

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

Is it indeterminate too?

I think so

:oldeyes:
No, it is not indeterminate. If the numerator approaches 0 and the denominator becomes unbounded, the limit is 0.
 
  • #10
105
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Oh, I see,,
Thanks
 

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