Chapter 2 Limits
You might not think limits would show up in a calculus course oriented toward application. Wrong! There are a lot of reasons why you need to understand the basic of limits. You should know these reasons, so here they are.
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You have already seen they show up in the definition of powers and logarithms when the exponent is not rational.
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The definition of derivative (instantaneous rate of change) is a limit.
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The number \(e \) is defined by a limit.
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Continuous compounding is a limit.
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Limits are needed to understand improper integrals, such as the integrals of probability densities.
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Infinite series, which we will discuss briefly, require limits.
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Discussing relative sizes of functions is really about limits.
