Evaluate the following limit : lim(x→π/3) (1 - tan x)/(x - π/4)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to\pi/3}\cfrac{1-tan\,\text x}{\text x-\frac{\pi}4} \)

lim(x→π/3) (1 - tan x)/(x - π/4)

Answer 1

Given, \(\lim\limits_{\text x \to\pi/3}\cfrac{1-tan\,\text x}{\text x-\frac{\pi}4} \)

Hence, \(\lim\limits_{\text x \to\pi/3}\cfrac{1-tan\,\text x}{\text x-\frac{\pi}4} \) = -2