Question

find the limit tan4x/x as x approaches 0.

Answer 1

Using l'Hopital's Rule, this limit is the same after taking the derivative of the numerator and denominator.

(d/dx)(tan(4x)) = 4sec^2(x)

(d/dx)x = 1

So rewrite the limit as 4sec^2(x) / 1 instead. Plug in 0, and your answer is 4.