Question

Use Newton's method to estimate the solutions of the equation 5x? *x-1=0. Start with X-1 for the loft solution and X 1 for the right solution. Find X, in each case Using Newton's method with X, - 1, the third approximation, xz, to the left solution to 5x2+x-10 (Round to four decimal places as needed.) Using Newton's method with x + 1, the the third approximation, xz, to the right solution to 5x? *x-1=08 (Round to four decimal places as needed.)

Answer 1

f(x) = 5x²+2-1 ['(x)= 10x+1 Newton method fran) Case xn- Xnt = (kx), f Ko= -1 Taking 71-1) 99999.0 - 1- =!x x2 = -0,6666 f'(-1) +(-0.6666) 2-0.56862 #'(-0.6666) $60-56862) 0:558372 t'.56062) -) Xze-0.56862 xo=1 Caseta Taking 2,- 1 - -(1) 0.545454 (1),f X2: hshshsia 0.38540 +10.545454) t 10.545454) x3 = 0.3590