Q$5.$ For the nominal values $x^{**}=3\mathrm{.}75,y^{**}=4\mathrm{.}24,$ and with $(x^{**})=(y^{**})=0\mathrm{.}005,$ bound the errors in calculating the following expressions:

a$)x^2{y}^2-xy$

b$)\sqrt[\phantom{2}]{x^2{y}^2}$

c$)x*sin(y)-cos(x)*cos(y)$

d$)(x-y{)}^2-e^{2x{y}^2}$