- #1

- 184

- 0

[itex]\int_0^{\infty}(t^{-2}e^t) dt[/itex]

What would be the first step here in determining convergence or divergence?

- Thread starter VitaX
- Start date

- #1

- 184

- 0

[itex]\int_0^{\infty}(t^{-2}e^t) dt[/itex]

What would be the first step here in determining convergence or divergence?

- #2

- 81

- 1

You can apply several tests. If you take integral calculus..... you use the comparsion test.. testing the bounds or evaluating a similar function via comparsion, test. You should find whether or not these converges.

[itex]\int_0^{\infty}(t^{-2}e^t) dt[/itex]

What would be the first step here in determining convergence or divergence?

- #3

lurflurf

Homework Helper

- 2,440

- 138

Try determining convergence or divergence of

[itex]\int_0^{\infty}(t^{-2}e^t) dt[/itex]

What would be the first step here in determining convergence or divergence?

[itex]\int_0^{1}t^{-2} dt[/itex]

and

[itex]\int_1^{\infty}e^t dt[/itex]

then deduce the convergence by comparison or otherwise of

[itex]\int_0^{\infty}t^{-2}e^t dt[/itex]

- #4

- 33

- 0

- #5

lurflurf

Homework Helper

- 2,440

- 138

- #6

- 184

- 0

So if both have no limit and diverge, then by comparison test the whole integrand diverges?Try determining convergence or divergence of

[itex]\int_0^{1}t^{-2} dt[/itex]

and

[itex]\int_1^{\infty}e^t dt[/itex]

then deduce the convergence by comparison or otherwise of

[itex]\int_0^{\infty}t^{-2}e^t dt[/itex]

Edit: Just noticed you have the limits a little different. How did you determine the limits to be those when evaluating them separately?

I get [itex]\int_0^1 t^{-2} dt = -1[/itex]

And [itex]\int_1^{\infty} e^t dt = \infty[/itex]

What would I determine from these exactly?

Last edited:

- #7

lurflurf

Homework Helper

- 2,440

- 138

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 10

- Views
- 33K

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 15

- Views
- 4K

- Last Post

- Replies
- 3

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 2K

- Replies
- 5

- Views
- 2K

- Replies
- 3

- Views
- 3K

- Last Post

- Replies
- 7

- Views
- 4K