Question

Let f(x) = sin(x) + 2xe® Use the secant method for finding the root. Conduct two iterations to estimate the root of the above equation. Let us assume the initial guesses of the root as xo -0.55, X1 0.66 < Answer:

Answer 1

$f(x)=sin(x)+2xe^x$

$x_{0}=-0.55$

$x_{1}=0.66$

$f(0.66)=3.167$

$f(-0.55)=-1.1573$

By Secant method

First iteration:

$x_{2}=x_{0}-f(x_{0})(\frac {x_{1}-x_{0}}{f(x_{1})-f(x_{0})})$

$x_{2}=-0.55-f(-0.55)(\frac {0.66+0.55}{f(0.66)-f(-0.55)})$

$x_{2}=-0.2262$

Second iteration:

$f(-0.2262)=-0.585$

$x_{3}=x_{1}-f(x_{1})(\frac {x_{2}-x_{1}}{f(x_{2})-f(x_{1})})$

$x_{3}=0.66-f(0.66)(\frac {-0.2262-0.66}{f(-0.2262)-f(0.66)})$

$x_{3}=-0.088$

So after two iterations, the root is

X= -0.088

answer.