Calculus Question

Question

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

Answer 1

f(x) = sqrx +1

y = sqrx +1

y= x^1/2 + 1

y' = dy/dx = (1/2)x^-1/2 = 1/2sqrx

dy = (1/2sqrx)dx

f(x) = sqrx + 1 is the top half of a rightward opening parabola, with vertex at (0,1).

y-1 = sqrx, square both sides

(y-1)^2 = x