Linear spproximation

Question

Use linear approximation and calculate the error for f(x)=sinx , a=0 , Δx=0.5 

 

Answer 1

Usually you solve a problem like this using

f(x + Δx) ≅ f(x) + f'(x)Δx, for small Δx

Then

sin(x + Δx) ≅ sin(x) + cos(x) Δx, for Δx << 1

 

Now you need a very small Δx ≠ 0.