Problem $1$:

A Nonlinear equations occur in almost all fields of engineering. For example, suppose a given task is expressed in the form $f(x)=0$ and the objective is to find values of $x$ that satisfy this condition. It is often difficult to find an explicit solution and an approximate solution is sought with the aid of mathematical software. Find a solution of

$f(x)=\frac{1}{\sqrt[\phantom{2}]{2}}{e}^{-\frac{1}{2}{x}^2}+\frac{1}{10}sin(x)$

A$.$ Write a program to compute the real roots $f(x)=0$ using Secant method, Newton's method and Bisection method.

B$.$ Show how many iterations of each method will converge to $5$ decimal places