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## Chapter 2 The Derivative

### 2.1 The Limit

• This section includes a summary of the limit, its applications, conditions for estimating an infinite series, and convergence.

• The limit is used in the estimation of infinite sums and in the definitions of the derivative and the integral. In general, the limit is used to describe closeness of a function to a value when the exact value cannot be identified. The limit is also used to determine if functions are continuous or discontinuous. Whether the graph of a given function is a smooth and continuous curve or line, or whether there are breaks or holes present can be determined using the limit.

• If the limx→a f(x) = L, then it is said that the function f(x) gets close to and may equal some number L as ...

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