Example 6: Polynomial

Given any polynomial

f(t) = a_ntⁿ + a_n-1t^n-1 + ... + a₁t + a₀

of degree n > 0, the limits as t approaches -∞ or + ∞ are as follows.

Suppose a_n > 0. When n is even,

lim_t→-∞f(t) = ∞, lim_t→∞f(t) = ∞.

When n is odd,

lim_t→-∞f(t) = -∞, lim_t→∞f(t) = ∞.

The signs are all reversed when a_n < 0. All these limits can be computed from