Show that 0 e x 2 e x for x 1 (Figure 12). Use
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Show that 0 ≤ e−x2 ≤ e−x for x ≥ 1 (Figure 12). Use the Comparison Test to show that ∫∞0 e−x2 dx converges. It suffices (why?) to make the comparison for x ≥ 1 because
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