- #1

- 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

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- Thread starter applestrudle
- Start date

- #1

- 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

- 17,593

- 8,584

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

- 63

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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

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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

- 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

- 74

- 6

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

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