Question

(3.968) power 3/2 find approximate value using differentiation

Answer 1

7.904 is the answer using differentiation

Answer 2

Answer:

Step-by-step explanation:

value of (3.968) power 3/2  using differentiation

Now, f(x + δx) = f(x) + g(x)* δx              [ Let df(x)/dx = g(x)]

Let f(x) = x

=> df(x)/dx = 3/2(x)3/2 -1

=> g(x) = 3/2*x1/2

Now f(3.968) = f(4 - 0.032)

                    = f(4) - 0.032 * g(4)

                    = 43/2 - 0.032 * (3/2) * 41/2

                    = 23 - 0.032 * (3/2) * 2

                    = 8 - 0.032 * 3

                    = 8 - 0.096

                    = 7.904

So, the approximate value of (3.968)3/2 = 7.904