Let y = sin ( 3 x ) . If Δ x = 0.1 at x = 0 , use linear approximation to estimate Δ y Δ y ≈ d y = Correct Find the percentage error error = %

Question

Let . If  at , use linear approximation to estimate    0.3Correct  Find the percentage errorerror =  % 

Answer 1

Δy ≈ dy = y'(0)·Δx; y'(x) = 3cos3x; y'(0) = 3cos0 = 3; Δy ≈ 3·0.1 = 0.3;

Exact value Δy = sin0.3 - sin0 = sin0.3 = 0.29552

So, percent error ε = (03 - 0.29552)/0.29552·100% = 1.516%