#$1)$ In this problem, you will consider a cantilever beam subjected to a vertical point load, P $,$ applied at its end, under large deflection conditions. Using your hand$-$out from Frisch$-$Fay, derive analytical expressions that will allow you to determine, for a given angle $=$ at the end of the beam:

a$)$ The applied load $P.$

b$)$ The vertical displacement of the end of the beam $($in the negative $y$ direction$).$

c$)$ The horizontal displacement of the end of the beam $($in the $x$ direction$).$