MATLAB PRACTICE EXAM $-$ PROBLEM $1$: A bar is placed between two walls that are kept at constant temperatures, $T_a=40C$ and $T_b=200C.$ For the steady$-$state case, the analytical solution of the heat transfer governing equation is the following function, where $T$ is the temperature in Celsius degrees and $x$ is the distance in meters along the bar.

$T=73\mathrm{.}4523e^{0\mathrm{.}1x}-53\mathrm{.}4523e^{-0\mathrm{.}1x}+20$

a$)$ Plot the temperature distribution along the distance $x$ for values of $x$ between $0$ and $10($the bar length $L=10m.$ Using the graph, estimate the location in the bar where the temperature reach $100C.$

b$)$ Using the bisection function file, determine the distance $x$ where the temperature is equal to $100C.$ Do the same with the Newton Raphson function file. Compare your results with the answer given by the MATLAB function fzero.

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