59-60 Use a graph to estimate the roots of the equation correct to one decimal place. Then use these estimates as the initial approximations in Newtons method to find the roots correct to six decimal places. (x4)2=lnx
Root of the given function correct to decimal places, using Newton’s Method.
The approximate root is
Graph of is shown below:
Since the graph of cuts the -axis, at exactly two points, therefore has two zeros.
The Newton’s formula is:.
. Let the initial approximation for first root be , then
Since upto decimal places, first approximate root is .
As we have seen that there are exactly two zeros of , so let’s consider approximation for second root, , then
Since upto decimal places, the approximate root is .