Question

How do you evaluate the limit `(tanx-sinx)/(xcosx)` as x approaches `0`?

Answer 1

`0`

Explanation:

`(tanx-sinx)/(xcosx)=sinx/x ((1-cosx)/cos^2x)`

`lim_(x->0)(tanx-sinx)/(xcosx)=lim_(x->0)sinx/x lim_(x->0)((1-cosx)/cos^2x)=1 cdot 0/1 = 0`