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)
the answer is f(x) = tan x, a = π/4 but I don't know how to get it. :S

Answer 1

Limit definition of the Derivative of a function:
`\lim_(h \to 0) (f(x+h)-f(x))/(h)` At x = a:
`\lim_(h \to0) (f(a+h)-f(a))/(h)`
If: h = x -π/4, we will have:
`\lim_(h \to \pi /4) (tan ( \pi /4 +h)-1)/(h)` When we compare it with a limit definition:
f( x )= tan x
f( a ) = 1
tan ( a ) = 1, a = π/4