Question

Lim as x approaches pi/4:

[(tan x - 1)/(x - pi/4)]

The limit represents the derivative of some function f at some number a. State such an f and a.

Answer 1

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

`\lim_(x \to \pi /4) (1)/(cos ^(2) x) = \\ = (1)/(cos ^(2) ( \pi /4)) = \\ (1)/(1/2)` = 2