Problem $1.($Newton$\text{'}$s method $-$ J$)$

Task b is to be done in python

Consider the function

$f(x)=logx+sin(x)$

We want to find the root of $f(x).$

a$)$ Compute two steps with Newton's method by hand, starting at $x_0=0\mathrm{.}5.$

b$)($J$)$ Implement Newton's method for the problem at hand and use it to find the root of $f(x)$ with error less than ${10}^{-3}.$ Use $x_0=0\mathrm{.}5$ as starting point.