Barrons AP Calculus

(a)

(b)

Figure  N2–6

Definition

The theorems that follow in §C of this chapter confirm the conjectures made
about limits of functions from their graphs.
Finally, if the function f(x) becomes infinite as x becomes infinite, then one or
more of the following may hold:

End Behavior of Polynomials

Every polynomial whose degree is greater than or equal to 1 becomes infinite as
x does. It becomes positively or negatively infinite, depending only on the sign
of the leading coefficient and the degree of the polynomial.

Example 7 __

For each function given below, describe .

f   (x) =   x^3     −   3x^2 +  7 x +   2

SOLUTION:.

g(x)    =   −4x^4 + 1,000,000x^3 +  100

SOLUTION:.