Question about indeterminate form

  • #1
105
3
why $$1^\infty$$ is indeterminate form?
 

Answers and Replies

  • #2
34,826
6,570
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
105
3
Thanks ,, I got it now
(:
 
  • #4
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
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
34,826
6,570
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
34,826
6,570
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.
 
  • Like
Likes Maged Saeed
  • #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

:oldeyes:
 
  • #9
34,826
6,570
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.
 
  • Like
Likes Maged Saeed
  • #10
105
3
Oh, I see,,
Thanks
 

Related Threads on Question about indeterminate form

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
9
Views
789
Top