Question:
Find the approximate value of (1.999)5.
Solution:
(1.999)5 = (2 – 0.001)5
Let x = 2 and ∆x = -0.001
Also, let y = x5
Differentiating both sides w.r.t, x, we get
dy/dx = 5x4 = 5(2)4 = 80
Now, ∆y = (dy/dx). ∆x = 80. (-0.001) = -0.080
And, (1.999)5 = y + ∆y
= x5 – 0.080 = (2)5 – 0.080 = 32 – 0.080 = 31.92
Therefore, approximate value of (1.999)5 is 31.92