Calculus Question

Question

Find the differential dy of function f(x) = √x+1 when x₀= 0 is used to approximate √1.1

Answer 1

dy = dx/2sqrt(x+1)

at x=0, dy=dx/2

when dx=.1, dy=.05 and therefore sqrt(1.1) is approximately 1.05

Note: it is sometimes easier to use the function y=x² for this approximation.