Question

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

lim (tan x − 1)/(x − π/4)
(x→π/4)

Answer 1

Limit definition of Derivative of a function at x=a : :

lim (f(a+h)-f(a))/h =

h->0

From limit definition i need just h in the denominator, so i can substitute, h = x-pi/4 as

x -> pi/4, h ->0

also x = pi/4+h

Comparing this with limit definition f(a+h) and tan (pi/4+h), we can figure out , f(x) = tan x , and a = pi/4. I hope that this is the answer that you were looking for and it has helped you.