Question

How do you find the linearization of `f(x)=sin2x` at x=pi/6?

Answer 1

Use the development of the Taylor series of the function

Explanation:

`f(x) = f(x_0)+f'(x_0)(x-x_0) + o((x-x_0^2)`

`sin(2x) ~= sin(pi/3) +2cos(pi/3)(x-pi/6)`

`sin(2x) ~= sqrt(3)/2+(x-pi/6)`