Homework SourseLet fxsqrtx find the differential dy of yfx use differential
Let f(x)=sqrt(x)
find the differential dy of y=f(x)
use differentials (or, what amounts to the same, linear approximation) and the fact that f(16)=4 to approximate sqrt(17)
find the differential dy of y=f(x)
use differentials (or, what amounts to the same, linear approximation) and the fact that f(16)=4 to approximate sqrt(17)
Solution
df/dx = lim h-> 0 { f(x+h) - f(x)}/h at x=a f(x+h ) = f(x) + h*df/dx (approximating linear condition i.e neglectinh f\"(x) and higher order derivatives ) f(16+1) = f(16) + 1* 1/sqrt(16) = 4+1/4 = 4.25 hence sqrt(17 ) nearly = 4.25
