Question

show that the linearization of sin(x) at 0= the linearization of tan(x) at 0

Answer 1

Linearization of sin(x) at x=0:
L= f(0)-f'(0)*(x-0)
L= 0 - cos(0*)x *the derivative of sin is cos
L= -x

Linearization of tan(x) at x=0
L= f(0)-f'(0)*x
L=0-f'(sec^2(0))*x *the derivative of tan is sec^2
L=-x