1
$\begingroup$

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

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

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.