Find the local linear approximation of the function $f(x)=\sqrt{2+x}$ at $\small{x_0=2}$, and use it to approximate $\sqrt{3.9}$ and $\sqrt{4.1}$.

(a) $f(x)=\sqrt{2+x}\approx$

(b) $\sqrt{3.9}\approx$

(c) $\sqrt{4.1}\approx$

For parts (b) and (c), you should enter your answer as a fraction. If you enter a decimal, make sure that it is correct to at least six decimal places.