Example 4

Find

lim_x→-∞ (x³ + 200x²).

We have x³ + 200x² = x²(x + 200). When H is negative infinite, H² is positive infinite and (H + 200) is negative infinite, so their product is negative infinite. Thus

lim_x→-∞ (x³ + 200x²) = -∞.

When

lim_x→cf(x) = ∞ or -∞,

the limit does not exist, because f(x) has no standard part. The infinity symbol is only used to indicate the behavior of f(x) and is not to be construed as a number.