- #1

- 475

- 1

## Homework Statement

[tex]\lim_{x \to \infty } \frac{\sin x}{x}[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]\lim_{x \to \infty } \frac{\sin x}{x}[/tex]

Substitute x = 1/u

[tex]\lim_{\frac{1}{u} \to 0 } \frac{\sin \frac{1}{u}}{\frac{1}{u}} = 1[/tex]

I know this is incorrect because intuitively I know that sinx will oscillate between 0 and 1, but the denominator will grow larger infinitely, therefore should theoretically approach 0 but that's just my thinking and no hard evidence.