- #1

applestrudle

- 63

- 0

## Homework Statement

lim x-> ∞ xsin(1/x)

## Homework Equations

## The Attempt at a Solution

I know that this is an ∞.0 type limit but I can't figure out how to change the sin function.

Thank you

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 applestrudle
- Start date

- #1

applestrudle

- 63

- 0

lim x-> ∞ xsin(1/x)

I know that this is an ∞.0 type limit but I can't figure out how to change the sin function.

Thank you

- #2

- 21,104

- 11,994

Hint

[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]

[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]

- #3

applestrudle

- 63

- 0

Hint

[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]

Ahh thank you! Then you use L'Hopitals Rule?

- #4

Mark44

Mentor

- 36,310

- 8,280

I wouldn't. This limit is related to this well-known limit

$$\lim_{t \to 0}\frac{sin(t)}{t}$$

$$\lim_{t \to 0}\frac{sin(t)}{t}$$

- #5

applestrudle

- 63

- 0

I wouldn't. This limit is related to this well-known limit

$$\lim_{t \to 0}\frac{sin(t)}{t}$$

What do you mean?

- #6

Legaldose

- 74

- 6

Hint 2: Use a substitution, then figure out what the appropriate change in the limit would be.

Share:

- Last Post

- Replies
- 4

- Views
- 2K

- Replies
- 5

- Views
- 857

- Last Post

- Replies
- 13

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 2K

- Replies
- 7

- Views
- 1K

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 823

- Last Post

- Replies
- 2

- Views
- 2K