What is the limit of $\frac{sin(sin\ x)}{x}$ as $x$ approaches infinity?

[planauts]

Homework Statement

$$\mathop{\lim}\limits_{a \to \infty} \frac{sin(sin\ x )}{x}$$

The Attempt at a Solution

I was thinking about starting off by multiplying by sin(x) over sin(x)

$$\mathop{\lim}\limits_{a \to \infty} \frac{sin(sin\ x )}{x} * \frac{sin\ x }{sin \ x}$$Don't know if that would help...

Thanks

 

[gb7nash]

Homework Statement

$$\mathop{\lim}\limits_{a \to \infty} \frac{sin(sin\ x )}{x}$$

The Attempt at a Solution

I was thinking about starting off by multiplying by sin(x) over sin(x)

$$\mathop{\lim}\limits_{a \to \infty} \frac{sin(sin\ x )}{x} * \frac{sin\ x }{sin \ x}$$


Don't know if that would help...

Thanks

What is a? Do you mean x? And (sinx)/x goes to 1 only if x is approaching 0. So I'm not sure this would work.

 

[zcd]

$$-1\leq\sin(x)\leq 1$$, so the value inside the parentheses restricts the outside sin() function, while the denominator grows without bound