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Home Limits, Analytic Geometry, and Approximations The ε, δ Condition for Limits Examples Example 4
 
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Example 4

In the limit

limx→∞ (x2 - x) = ∞.

find a B > 0 such that whenever

x > B, x2 - x > 10,000.

This time we assume x > B and get an inequality for x2 - x. We may assume B > 1.

05_limits_g_approx-407.gif

Now take a B such that

B2 - B > 10,000.

The number B = 200 will do, because

(200)2 - 200 = 39800.

Thus whenever x > 200, x2 - x > 10,000.
Home Limits, Analytic Geometry, and Approximations The ε, δ Condition for Limits Examples Example 4

Last Update: 2006-11-15