Asymptotic analysis

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In mathematical analysis, asymptotic analysis, also known as asymptotics, is the development and application of methods that generate an approximate analytical solution to a mathematical problem when a variable or parameter assumes a value that is large, small or near a specified value. An example of asymptotic analysis is function approximation. For example, the function y ~ ( x ) = x {\textstyle {\widetilde {y}}(x)=x} accurately approximates the function y ( x ) = x + e − x {\textstyle y(x)=x+e^{-x}} for large positive x {\textstyle x} values (Figure 1). For any desired accuracy, there is a corresponding range...

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