Show that if x x1 1 and y y1 2 where 1 SolutionX Y x xe

Show that if x = x(1 + _1) and y = y(1 + _2), where |_1|

Solution

X -Y = x+ xe₁ - y -ye₂   

= x-y +(x-y) e - xe+xe₁+ye -ye₂  (addingandsubtracting xe , ye )

=(x-y) (1+e) + x(e₁  -e) -y(e₂ -e) selecy e =₍ e₁+e_{2)/2 andthe difference}e₁ -e₂ almost=0

= (x-y )(1_+e )