Roots Finding

A chemical process follows the equation given bellow

$\frac{dh(t)}{dt}=\frac{1}{A}(F_{in}-k\sqrt[\phantom{2}]{g}\sqrt[\phantom{2}]{h(t)})$

for $F_{in}=10\mathrm{.}15\frac{m^3}{m}in,A=3m^2,k=0\mathrm{.}17s^2\frac{m^2}{\text{m}\text{i}\text{n}\text{k}\text{g}},=1000k\frac{g}{m^3},g=9\mathrm{.}8\frac{m}{s^2}.$

Determine $h(t)$ at steady state by using Bisection, Fixed position, NewtonRaphson and Quasi Newton$-$Raphson $($Secant$)$ Methods by hand for $5$ steps for each method.

Analyze $h(t)$ at steady state by using Bisection, Fixed position, NewtonRaphson and Quasi Newton$-$Raphson $($Secant$)$ Methods by Python.

Compare the answer to analytical solution

Submit the homework report before $15$ February $2024.$ Late submission will get a discounted mark according according to number of delay to the due date.