Question

How do you evaluate the limit `sin(6x)/cos(4x)` as x approaches `0`?

Answer 1

`lim_(x rarr 0) sin(6x)/cos(4x) = 0`

Explanation:

We seek:

`L = lim_(x rarr 0) sin(6x)/cos(4x)`

We note that both `sintheta` and `cos theta` are both continuous well behaved function and that both are defined when `theta =0`

Thus:

`L = (lim_(x rarr 0) sin(6x))/(lim_(x rarr 0) cos(4x)) = sin0/cos0 = 0/1 = 0`