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 .