Figure 2 Figure 4 1. Recall the point-slope form of the equation of a line of slope m passing through (x., y.) is y yl = m(x x1). Use this equation to verify that the line tangent to the curve y = f(x) at x = x is y=f(xn]+f'(xnl(xIH)- (1) 2. Assume the tangent line represented by equation (1] intersects the xaxis at x = x\" H and verify that updated approximation approximation approximation PM FM .--. f (x) xn+l = In _ . ' (2) f (x5) W approximation Using equation (2) with n = I], l, 2, 3, ..., the current approximation x\" is used to obtain a (hopefully) improved approximation xm . The resulting sequence of approximations {xu, x:, x:, .. .} ocn approaches a root of f very quickly. Using N ewton's Method 3. Let x) = x3 5x+1. a. Show that Newton's method takes the form 3 =1: _xn SIN-H, (3) 3x\" 5 where n = 0, 1,2, 3, b. Use equation (3) to find I] if x0 = 4.5 . c. Find x2 using the value of II found in part (b). d. Find x3 using the value of x2 found in part (c). c. Graphf using the window [0,5]>