Introduction to Limits

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Introduction to Limits

• Numerical, Graphical, Algebraic
• Marlow Dorrough
• University of Mississippi

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Immediate Objective to understand an
idea
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Long-Range Objective to express the idea in
algebraic language
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Super Long-Range Objective to
understand and enjoy the vast tapestry of ideas
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Ready?
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If a limit involved no more than plugging a
number into an equation, we could hardly call it
the central idea that distinguishes calculus
from algebra and trigonometry (p.73, Thomas
Calculus). So there must be more to the story
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Piecewise-defined functions
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Infinite Limits
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Dont be confused about vertical asymptotes -
they dont occur just because the denominator is
zero. The limit must actually be infinite.
Consider two earlier examples with no vertical
asymptotic behavior
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Limits at Infinity
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