​ Consider the function y = f√x 1. If x = 0.0036 and ∆x = 0.0001 find ∆y. ​2. Hence approximate √.0037 using differentials

Question

Consider the function y = f\(\sqrt{x}\)

1. If x = 0.0036 and ∆x = 0.0001 find ∆y. 
2. Hence approximate \(\sqrt{.0037}\) using differentials.

Answer 1

1. Let 

x = .0036, ∆x = 0.0001

2. (1) ⇒ \(\sqrt{.0037}\) = .000833 + .06 = .060833.