Use Newtons Method to estimate squareroot 5 Use x02 and perf

Use Newton\'s Method to estimate squareroot 5 Use x0=2 and perform 2 iterations. Compare Newton\'s estimate to the exact root.=

Solution

here the vaiue is given X0= 2 nad f(x0)= 8

At point (2,8) the line of tangent to the slope F has F\'(x)= 2(2)=4,

so the equation of tangent is y-8 = 4(x-2)

setting y=0 we can find the x =0

here that equal to X1=0

the value of X1 is closer root but not the actual root . by using X1 we can find x2 in similar manner

so we get X2 = 2.37.