If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?

The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error observed at $${2^{nd}}$$ iteration is ___________.

When the Newton-Raphson method is applied to solve the equation $$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$ the solution at the end of the first iteration with the initial value as $${x_0} = 1.2$$ is

Let $$\,{x^2} - 117 = 0.\,\,$$ The iterative steps for the solution using Newton -Raphson's method is given by