Chapter 1
Building Blocks of Calculus
By Boundless
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Functions relate a set of inputs to a set of outputs such that each input is related to exactly one output. Graphs can be used to represent these relationships pictorially.
Linear and quadratic functions make lines and a parabola, respectively, when graphed and are some of the simplest functional forms.
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Trigonometric functions are functions of an angle, relating the angles of a triangle to the lengths of the sides of a triangle.
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An inverse function is a function that undoes another function: For a function
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Both exponential and logarithmic functions are widely used in scientific and engineering applications.
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For numerical calculations and graphing, scientific calculators and personal computers are commonly used in classes and laboratories.
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Iinstantaneous velocity can be obtained from a position-time curve of a moving object.
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The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of a function near a particular input.
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Limits of functions can often be determined using simple laws, such as L'Hôpital's rule and squeeze theorem.
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The
A continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output.
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For a real-valued function expressed in terms of other functions, limit values may be computed via algebraic operations.
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There are several limits of special interest involving trigonometric functions.
For a real-valued continuous function
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Limits involving infinity can be formally defined using a slight variation of the