Bourbaki

Example 5

Tag 08EB, permanent. Cite it as [Bourbaki, Tag 08EB].

Functions of a Real Variable, chapter V, § 1. COMPARISON OF FUNCTIONS ON A FILTERED SET

As (x,y)(x, y) approaches (0,0)(0, 0) in R2\mathbf{R}^2 one has

sin⁡2x+sin⁡2y∼x2+y2. \sqrt{\sin^2 x + \sin^2 y} \sim \sqrt{x^2 + y^2}.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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Transcribed from the printed volume. Not translated.