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Infinite Limits

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

05_limits_g_approx-1.gif f(x) = L means f(x) ≈ L whenever x ≈ c but x ≠ c.

05_limits_g_approx-2.gif f(x) = L means f(x) ≈ L whenever x ≈ c but x > c.

05_limits_g_approx-3.gif f(x) = L means f(x) ≈ L whenever x ≈ c but x < c.

The limit notation

limx→∞f(x) = L

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

limx→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.

05_limits_g_approx-10.gif

Figure 5.1.1

Examples 1 & 2: Limits


Last Update: 2006-11-14