Question

The limit as x approaches 0 of
(tan2x)/3x = ?

Answer 1

we know that
lim tanØ/Ø , as Ø ---> 0 = 1

so change your question to resemble that expression

let Ø = 2x
x = Ø/2
3x = 3Ø/2

then tan 2x/(3x) = tanØ/(3Ø/2
= (2/3) ( tanØ/Ø)

so lim 2x/(3x) = (2/3)(1) = 2/3