Linear approximation is used when the value needed is close to a known value. Here, we know sqrt(9)=3. Let f(x)=sqrt(x) f'(x)=1/(2sqrt(x)) Apply linear approximation f(9.05)=f(9)+f'(x)dx =sqrt(9)+0.05/(2sqrt(9)) =3+.05/(6) =3.008333 exact value is 3.008322, estimate is off by .0004%
