Differential geometry

Osculating plane

In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word osculate is from the Latin osculatus which is a past participle of osculari, meaning to kiss. An osculating plane is thus a plane which "kisses" a submanifold. The osculating plane in the geometry of Euclidean space curves can be described in terms of the Frenet-Serret formulas as the linear span of the tangent and normal vectors. (Wikipedia).

Osculating plane
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Condensing mulitple logarithms

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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From playlist Summer of Math Exposition 2 videos

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From playlist Multivariable Calculus

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Condensing a large logarithmic expression to one single logarithm

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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From playlist Calculus 3 (Full Length Videos)

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Condensing logarithms with multiple parentheses

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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From playlist Summer of Math Exposition 2 videos

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Condensing a logarithmic expression with parenthesis

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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From playlist Calculus III

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Condensing logarithmic expressions

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

Video thumbnail

Condensing logarithmic expressions

πŸ‘‰ Learn how to condense logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the expanded form to a condensed form. Knowledge of the logarithm law

From playlist Condense Logarithms with Brackets

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From playlist MIT Calculus Revisited: Multivariable Calculus

Related pages

Contact (mathematics) | Submanifold | Linear span | Affine space | Mathematics | Differential geometry | Euclidean space | Normal plane (geometry) | Osculating circle