Question

Lim as x approaches pi/4:

Answer 1

$\lim_{x \to \pi /4} \frac{tan x - 1}{x- \pi /4} = \frac{0}{0}$
With L` Hospital`s Rule ( ( tan x ) ` = 1/ cos^2 x ) :
$\lim_{x \to \pi /4} \frac{1}{cos ^{2} x} = \\ = \frac{1}{cos ^{2} ( \pi /4)} = \\ \frac{1}{1/2}$   =  2