Trig Limits

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

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gb7nash
Homework Helper

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