Infinite Limits

Up to this point we have studied three types of limits:

f(x) = L means f(x) ≈ L whenever x ≈ c but x ≠ c.

f(x) = L means f(x) ≈ L whenever x ≈ c but x > c.

f(x) = L means f(x) ≈ L whenever x ≈ c but x < c.

The limit notation

lim_x→∞f(x) = L

means that whenever H is positive infinite, f(H) ≈ L (Figure 5.1.1(a)).

lim_x→cf(x) = -∞

means that whenever x ≈ c and x ≠ c, f(x) is negative infinite (Figure 5.1.1(b)). The various other combinations have the meanings which one would expect.

Figure 5.1.1

Examples 1 & 2: Limits