What is the limit of tanx/x as x approaches zero?
and
What is the limit of sin2x/sin3x as x approaches zero?
L'Hopital's rule is not necessaryhint: $\displaystyle \frac {\tan x}x = \frac {\sin x}{x \cos x} = \frac 1{\cos x} \cdot \frac {\sin x}x$
and you should be able to handle that. think "special limit"
use the addition formula for sine to simplify. you may have to do it more than onceWhat is the limit of sin2x/sin3x as x approaches zero?
$\displaystyle \sin (A + B) = \sin A \cos B + \sin B \cos A$
in particular, $\displaystyle \sin 2A = 2 \sin A \cos A$ and $\displaystyle \sin 3A = \sin (2A + A)$