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Exponentials![]() ![]() ![]() ![]() Powers and Roots![]() ![]() ![]() ![]() ![]() Properties of LimitsThe limit of a sum is the sum of the limits:![]() The limit of a product is the product of the limits:![]() The limit of a quotient is the quotient of the limits:![]() Squeeze Theorem:![]() AKA the "Flyswatter Theorem". Why?![]() ![]() Ratios of PolynomialsThe limiting behavior of the ratio of two polynomials depends on the degree of the polynomials. The polynomial of higher degree "wins". If their degrees are the same, then the limit is the ratio of the leading coefficients.![]() ![]() ![]() | ||||||||
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New Series From OldMultiply by a constant:
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> > | Useful LimitsExponentials![]() ![]() ![]() ![]() Powers and Roots![]() ![]() ![]() ![]() ![]() Properties of LimitsThe limit of a sum is the sum of the limits:![]() The limit of a product is the product of the limits:![]() The limit of a quotient is the quotient of the limits:![]() Squeeze Theorem:![]() AKA the "Flyswatter Theorem". Why?![]() ![]() Ratios of PolynomialsThe limiting behavior of the ratio of two polynomials depends on the degree of the polynomials. The polynomial of higher degree "wins". If their degrees are the same, then the limit is the ratio of the leading coefficients.![]() ![]() ![]() | |||||||
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Error during latex2img: ERROR: problems during latex INPUT: \documentclass[fleqn,12pt]{article} \usepackage{amsmath} \usepackage[normal]{xcolor} \setlength{\mathindent}{0cm} \definecolor{teal}{rgb}{0,0.5,0.5} \definecolor{navy}{rgb}{0,0,0.5} \definecolor{aqua}{rgb}{0,1,1} \definecolor{lime}{rgb}{0,1,0} \definecolor{maroon}{rgb}{0.5,0,0} \definecolor{silver}{gray}{0.75} \usepackage{latexsym} \begin{document} \pagestyle{empty} \pagecolor{white} { \color{black} \begin{math}\displaystyle n \rarrow \infty\end{math} } \clearpage \end{document} STDERR: This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013) restricted \write18 enabled. entering extended mode (/tmp/4opd68QOo9/IPPjc6qFcQ LaTeX2e <2011/06/27> Babel | |||||||
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-- DickFurnas - 21 Oct 2008 |
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Error during latex2img: ERROR: problems during latex INPUT: \documentclass[fleqn,12pt]{article} \usepackage{amsmath} \usepackage[normal]{xcolor} \setlength{\mathindent}{0cm} \definecolor{teal}{rgb}{0,0.5,0.5} \definecolor{navy}{rgb}{0,0,0.5} \definecolor{aqua}{rgb}{0,1,1} \definecolor{lime}{rgb}{0,1,0} \definecolor{maroon}{rgb}{0.5,0,0} \definecolor{silver}{gray}{0.75} \usepackage{latexsym} \begin{document} \pagestyle{empty} \pagecolor{white} { \color{black} \begin{math}\displaystyle n \rarrow \infty\end{math} } \clearpage \end{document} STDERR: This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013) restricted \write18 enabled. entering extended mode (/tmp/cIfvGPD464/bAJ7jrjY94 LaTeX2e <2011/06/27> Babel | |||||||
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Infinite Series: A Synopsis
Famous SeriesGeometric Series![]()
P-Series![]()
Harmonic Series![]()
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![]() Exponential![]()
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![]() ln (1+x)![]() ![]() arctan (x)![]() ![]() -- DickFurnas - 21 Oct 2008 |