$5\mathrm{.}12.$ Let

$($

$)$ and let

$?$

$f()=H(181$

$4)$

where $His$ the Heaviside step function that $is$ zero for inputs less than zero and unity

for nonnegative inputs Tasks: $(1)$ Describe and sketch the surface defined $by$ the function

$f(xct),$ where $c=2is$ the wave speed, $on$ the domain $(xt)[41][02].(2)$

Determine a function that gives the location $of$ the left leading edge $=1$

profile $as$ a function $oft.(3)$ Where $is$ the leading edge located $atift=1$