Hint: use two different sequences to show that their result are different thus the limit DNE

4. Limits can measure the rate at which functions tend to zero (or infinity) and polynomials are your favourite functions of all time. Let a], ..., a, EN and let A E N. You will compare the rate at which the monomial al . . . xan and the norm | |x| |4 tend to zero as x = (X1, . . ., Xn) - 0. X 1 a1 . . . xan (4a) Prove that if an + . . . + an A then lim n does not exist. x-0