Question

why lim -x/tan(3x) become lim[-1/3(sec3x)^2]?

Answer 1

This is an example of l'Hopital's rule, differentiating numerator and denominator ...

Answer 2

\[ \frac{d}{dx} \tan(3x) = 3\sec(3x)^2 \]

Answer 3

okay.

Answer 4

looks good to me!

Answer 5

\[\frac{d}{dx} \tan(3x)=3 \sec^2(3x)\]