Question

How do you evaluate the limit `sin(5x)/sin(6x)` as x approaches `0`?

Answer 1

`5/6`

Explanation:

`lim_(x to 0) sin(5x)/sin(6x)`

we will use fundamental trig result: `lim_(z to 0) ( sin z)/z = 1`

`= lim_(x to 0) (5(5sin(5x))/(5x))/(6(sin(6x))/(6x)) = 5/6`