3 Let y(x) = = 1/2 ( x + 2²/1) Show that a.) x* = √3 is a fixed-point for . Are there other fixed-points? b.) the fixed-

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3 Let Y X 1 2 X 2 1 Show That A X 3 Is A Fixed Point For Are There Other Fixed Points B The Fixed 1 (67.45 KiB) Viewed 36 times

3 Let y(x) = = 1/2 ( x + 2²/1) Show that a.) x* = √3 is a fixed-point for . Are there other fixed-points? b.) the fixed-point method using converges to √√3 for any x₁ = I=(√3, ∞) . c.) the fixed-point method using converges to √3 for any xo >0 . 1 d.) if > 0 then k+1 √3 (xk √3)², k = 0,1,2,...,n . Determine the order of the method. = 2xk e.) the fixed-point method is in fact a Newton's method in disguise. Apply Newton to f(x) = x² – 3, x>0 ·