Given: f(x) = 9 cos (2x)
The differential equation is df = - 18 sin(2x) dx
When x contrasts from π/6 to π/6 + 01, then dx = 0.1.
The variation in f is δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559
The computation in the change in f directly:
f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638
Direct computation of δf is near to the real value but in error.
The two outcomes will be closer as dx gets smaller.
Answer would be:
δf = -1.559 (correct answer)
δf = -1.638 (approximate answer)
