- #1

- 105

- 3

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Maged Saeed
- Start date

- #1

- 105

- 3

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

- #2

Mark44

Mentor

- 34,826

- 6,570

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

- 105

- 3

Thanks ,, I got it now

(:

(:

- #4

- 16,744

- 8,623

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

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

- #5

Mentallic

Homework Helper

- 3,798

- 94

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

Mark44

Mentor

- 34,826

- 6,570

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

Mentor

- 34,826

- 6,570

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

- 105

- 3

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

- #9

Mark44

Mentor

- 34,826

- 6,570

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

- 105

- 3

Oh, I see,,

Thanks

Thanks

Share: