Final answer:
The best way to approximate √(x+δ) - √(x) is 0.006.
Step-by-step explanation:
To approximate √(x+δ) - √(x), we can make use of the binomial approximation. By assuming that δ is very small compared to x, we can simplify the expression.
Let's assume that x = 0.2 and δ = 0.012. The approximation becomes:
- (x + δ)√(1 + δ/x) - x√(1)
- 0.2√(1 + 0.012/0.2) - 0.2√(1)
- 0.2√(1.06) - 0.2√(1)
- 0.2(1 + 0.06/2) - 0.2
- 0.2 + 0.006 - 0.2
- 0.006
Therefore, the best way to approximate √(x+δ) - √(x) is 0.006.