Answer 4b), 4 simply provides background info and sets up 4b to be answered. I also provided the formal definition of a limit for your aid.

4. Limits can measure the rate at which functions tend to zero (or infinity) and polynomials are your favourite functions of all time. Let a1, ..., an E N and let A E N*. You will compare the rate at which the monomial x 1 . .. xan and the norm ||x|4 tend to zero as x = (X1, . .., Xn) - 0. X 1 a1 . ..xan (4b) Use the formal &-d definition of the limit to prove that if al + .. . + an > A, then lim = 0. x-0 That is, the monomial x 1 . . . xan tends to zero faster than | |x| |4 when its degree a, + ... + a, exceeds A. Definition 2.6.1 Let f : A-> R" be a function with A C R". Let a E R" be a limit point of A and let b E RM. Define b to be the limit of f at a provided -3> |19-(x)fll ||0-x|> 0V xA "T's 0