Question

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

Answer 1

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