please help me write five challenge calculus equations. in these equations, the overall answers need to be $1,2,3,1/2,1/3,$or $3/2.$you can choose from these topics, but you must choose a different topic per question: limits at infinity$/$infinite limits$,$derivatives of product rule$/$quotient rule$/$chain rule, derivatives of exponential$/$log equations. these must be challenging, multi$-$step problems, and the resulting answers must be different values in the ones that i provided. each question must use a different topic $($no two equations out of the three should be the same topic out of those listed$)$