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What are asymptotes?

What are asymptotes? Here are some definitions.

Noun
  1. plural of asymptote
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Examples
An alternative form of correlation based on the power-mean of the bounding asymptotes has two significant advantages.
If you're the President, and you're in line with Congress, your approval rating inevitably asymptotes toward that ten per cent.
Forget about complex numbers, differentiating sine x, asymptotes and group theory.
The distributions become approximately exponential when the curve shown here asymptotes.
In book two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics.
She was up in her attic one afternoon, trying to concentrate on where to place her asymptotes on her hyperbola, but her mind traveled elsewhere.

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