help please....?

Question

Use differentials to estimate the value of square root of 99.5.

and it's not 9.9749689

Answer 1

Find the closest square root to that value. (100)
Use the formula

f(x) - f'(x)(x - a) where x = 100 and a = 99.5
f'(x) = 1/(2(x)^(1/2))

You get 10 - 1/2(100)^(1/2) * (100 - 99.5)

10 - 1/20 (.5) = 9.975

Answer 2

sqrt(99.5)= 10 - 0.5 d(sqrt(y)/dx) for y=10
d sqrt(y)/dx = 1/2 y^(-1/2) = 1/20
sqrt(99.5)= 10 - 0.5(0.05)= 9.975