limit x->+inf sin(sin(x))/x — step-by-step solution

Let's evaluate the limit of

\frac{\sin (\sin (x))}{x}

when

x \to +∞

The limit of

\sin (x)

does not exist but is bounded in

[-1, 1]

when

x \to +∞

The limit of

\sin (\sin (x))

does not exist but is bounded in

[-1, 1]

when

x \to +∞

ⓘ A bounded quantity divided by a quantity that grows without bound tends to 0

So the limit of

\frac{\sin (\sin (x))}{x}

0

when

x \to +∞

▶Limit:

0