Question

lim x-->0 sin5x/x

How do I find the limit using:
lim x=0 sinx/x=1

Answer 1

you need same angle to tend to 0, which is with sine function, and the same denominator,
so, when x-->0, 5x also -->0
for denominator, you can do this adjustment,
\(\large 5 \dfrac{\sin 5x}{5x}\)

Answer 2

now you have,
\(\large 5\lim \limits_{5x \rightarrow 0 } \dfrac{\sin 5x}{5x}\)
which is of the standard form.
can you solve now ?

Answer 3

To me, that now looks like this:
5 lim 5x-->0 sin 1

So is it 1/5?

Answer 4

no....