solve the triple integral: $$ \int_0^\infty \int_0^\infty\mathrm{e}^{-y},\mathrm{d}x\mathrm{d}y $$

for this question one has to solve the inner integral first and then the outer integral. A lot of tricky questions can be made from this.

solve for x: (x^2-3x+2)^.5 + (x^2-5x+4)^.5=0

the answer is x=1 the only possibility is when both of these terms are zero. so solve for the roots of both the quadratic terms and reach to the answer.

if you are given a karnaugh map of F, then find a min-term form of F inverse.

first, find F inverse using karnaugh map, then find its max term form, and then take its dual