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## Main Question or Discussion Point

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

- Thread starter Maged Saeed
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- #1

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

- #2

Mark44

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

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

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Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.why $$1^\infty$$ is indeterminate form?

- #5

Mentallic

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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.Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.

- #6

Mark44

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I agree. It's not indeterminate because you can determine what the limit will be.I don't believe that [itex]1/\infty[/itex] is an indeterminate form because its value cannot be anything other than 0.

- #7

Mark44

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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.Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.

- #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.

Me too .I agree. It's not indeterminate because you can determine what the limit will be.

How about

$$\frac{0}{\infty}$$

Is it indeterminate too?

I think so

- #9

Mark44

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No, it is not indeterminate. If the numerator approaches 0 and the denominator becomes unbounded, the limit is 0.Me too .

How about

$$\frac{0}{\infty}$$

Is it indeterminate too?

I think so

- #10

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Oh, I see,,

Thanks

Thanks

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