Find k>0 and m in so that (7n^3)+13n ≤ kn^3 for all integers n≥m
Consider k=8
The inequaliy simplifies to 13n<=n^3 This is true for all n>=3 Taking the derivative gives us 13 and 2n^2 which is enough to show that 13n will never catch up once the right hand side pulls ahead. If k is not restricted to integers any number greater than 7 will do though the m will change depending on which k you choose.