# Linear Approximation of a quantity

How do i proceed estimating this quantity using Linear Approximation?

$$\dfrac{1}{\sqrt{95}}-\dfrac{1}{\sqrt{99}}$$

My understanding is that I need to decide what the function is, find a 'nice' point a, the deviation h, and it's prime and then use this formula

$${\Delta}{f}{\approx} {f'(a)h}$$

## 2 Answers

Hint

$$\dfrac{1}{\sqrt{95}}-\dfrac{1}{\sqrt{99}}=\dfrac{1}{\sqrt{100-5}}-\dfrac{1}{\sqrt{100-1}}=\frac{1}{10}\big(\dfrac{1}{\sqrt{1-0.05}}-\dfrac{1}{\sqrt{1-0.01}}\big)$$

I am sure that you see the function and that you can take from here.

There are probably better solutions, but the obvious one is $$f(x)=\frac{1}{\sqrt{100-5x}}-\frac{1}{\sqrt{100-x}}.$$ "Nice" point and the rest should be clear now.