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Título: Examples of Functions


Descripción automática: In this video, the presenter introduces key mathematical functions and their graphical representations, which are essential for early courses at a university. The discussion begins with the quadratic function \( x^2 \), demonstrating how positive and negative values of \( x \) result in a parabolic graph on the positive side of the y-axis.

The cubic function \( x^3 \) is explored next, highlighting its faster growth compared to the quadratic function and its distinct shape due to negative \( x \) values producing negative outputs. The square root function is then covered, noting its limitation to non-negative \( x \) values and its common use in calculating areas between curves.

The video progresses to periodic functions, explaining the \( 2\pi \)-periodic nature of the sine and cosine functions, their graphical patterns, and their relationship with each other through phase shifts. The complexities of graphing the tangent function are described, with a focus on its vertical asymptotes and undefined values at certain points.

Lastly, the presenter discusses hyperbolic functions, comparing the hyperbolic sine to the cubic function and the hyperbolic cosine to the parabolic curve, while emphasizing their much faster growth rates. The visual resemblance between these functions and more familiar ones is used as a memorization aid. The video concludes with the hope that understanding these graphical representations will assist students in solving future mathematical problems.

Autor/a: Moll López Santiago Emmanuel

Curso: Este vídeo es el 6/28 del curso MOOC Math Fundamentals: Derivatives.    • MOOC Math Fundamentals: Derivatives  
Inscríbete en: https://www.edx.org/es/learn/math/uni...


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