Question

How do you evaluate the limit `sin(x/5)/x` as x approaches `0`?

Answer 1

I got `1/5`

Explanation:

Solving it directly would give us the indeterminate form `0/0`.
We can use de l'Hospital Rule by deriving top and bottom and then applying the limit:

`lim_(x->0)(sin(x/5))/x=lim_(x->0)(1/5cos(x/5))/1=`

As `x->0` we will get:

`=1/5cos(0)/1=1/5`