State such an f and a

Question

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

lim 𝜃→𝜋

3

cos(𝜃) − 1

2

𝜃 − 𝜋

3

Answer 1

f'(a) = lim _x→a [ (f(x) - f(a)) / (x - a) ]

lim_θ→π/3 [(cosθ - cos(π/3)) / ( θ - π/3)] = lim_θ→π/3 [(cosθ - 1/2) / (θ - π/3)] = f'(π/3), where f(θ) = cosθ and

a = π/3

So, the value of the limit is f'(π/3) = -sin(π/3) = -√3 / 2