Question

How do you find the limit of `(Sin5x) / 5` as x approaches 0?

Answer 1

We know that `lim_(x->0) sinx/x=1` hence

#lim_(x->0) x*sin(5x)/(5x)=lim_(x->0)x*(lim_(x->0) sin(5x)/(5x))= 0*1=0#

Answer 2

`0`

Explanation:

We can plug in `0` straightaway, since it doesn't cause any domain errors:

`lim_(xrarr0)sin(5x)/5=sin(5*0)/5=sin0/5=0`

Examining the graph of `sin(5x)/5` reveals the point `(0,0)` is on the function:

graph{sin(5x)/5 [-1.2, 1.2, -0.599, 0.601]}