Answer
$\sqrt {2}-\sqrt {1}\approx\frac{1}{2}$, the actual value is 0.41421356 (to 8 decimal places).
$\sqrt {101}-\sqrt {100}\approx0.05$, the actual value is 0.0498756 (to 6 decimal places).
Work Step by Step
Given: $ f(x)=\sqrt x $ and $ h=1$.
As $ h=1$, we can use Equation (3) which is
$ f(x_{0}+1)-f(x_{0})\approx f'(x_{0})$
When $ x_{0}=1$, we get
$\sqrt {2}-\sqrt {1}\approx f'(1)=\frac{1}{2\sqrt 1}=\frac{1}{2}$
The actual value is 0.41421356 (to 8 decimal places)
When $ x_{0}=100$, we have
$\sqrt {101}-\sqrt {100}\approx\frac{1}{2\sqrt {100}}=0.05$
The actual value is 0.0498756 (to 6 decimal places)
