Suppose f : D --> R is a function whose domain contains (-infinity, a) for some a R. We define to mean for all M >0 there exists K <0 such that

.

We define to mean for all M < 0 there exists K < 0 such that

.

Suppose n is a positive integer and let be a polynomial function defined by

for all x R.

(a) Suppose that n is odd and an is positive. Prove that . (Hint: You may use that for all x < -1)

(b) Prove that if n is even and an is positive then . (Hint: replacing P with -P) Do not do this

= = .

(c) Prove that if n is even and an is positive then .