Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2004 / Paper 2 / 9 / b / ii / Solution

Set $h=k/100$ and $j=m/100$. The exact ratio is $(1+h{)}^p(1+j{)}^q$. Multiplying the two binomial series and retaining total degree at most two gives the second-order relative change of a monomial:Multiply by one hundred to express the change as a percentage:The cross term accounts for the simultaneous changes in both inputs and cannot be recovered by simply adding their separate second-order percentage changes.