Question

find lim x-->0 (sin(3x))/x

Answer 1

\[\lim_{x \rightarrow 0} \frac{ \sin(3x) }{ x }\]

Answer 2

this need to be rewritten and use the following limit fact

\[\lim_{\theta \rightarrow 0} \frac{\sin(\theta)}{\theta} = 1\]

so rewriting the fraction so the denominator is the same as the angle

it can be written as

\[\lim_{x \rightarrow 0}\frac{3\sin(3x)}{3x}\]

I let h = 3x in the limit below...

\[\ = 3 \times \lim_{h \rightarrow 0}\frac{\sin(h)}{h} = 3 \times 1\]

Answer 3

ok thanks.