Question

Solve the equation $x=e^{-x}$ using Newton-Raphson method. Starting with an initial guess values $x_0=0$, the value of x after first iteration is .

• A. -0.050
• B. -1
• C. 0.50
• D. 1

Answer 1

The correct option is C 0.50

$f\left(x\right)=x-e^{-x}$
Newton Raphson method
First iteration, $x_1=x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}$
Here, $f^{\prime }\left(x\right)=1+e^{-x}$
$x_1=0-\frac{f\left(0\right)}{f^{\prime }\left(0\right)}$
=$\frac{-(0-e^{-0})}{1+e^{-0}}$
=$\frac{1}{2}=0.50$