linear approximation at a point
[ˈlɪn.i.ər ə.ˈprɑk.sɪ.ˈmeɪ.ʃən æt ə pɔɪnt]
nounpl: linear approximations at a point
aproximação linear em um ponto
1. A mathematical technique that uses the tangent line to a curve at a specific point to estimate the value of a function near that point
The linear approximation at a point provides a first-order Taylor polynomial to approximate the function's behavior locally.
A aproximação linear em um ponto fornece um polinômio de Taylor de primeira ordem para aproximar o comportamento da função localmente.
2. The process of finding a linear (first-degree) function that best represents a nonlinear function near a given point
Using linear approximation at a point, we can estimate f(x) ≈ f(a) + f'(a)(x - a) near x = a.
Usando aproximação linear em um ponto, podemos estimar f(x) ≈ f(a) + f'(a)(x - a) próximo a x = a.
3. In calculus, the tangent line equation used to approximate function values for points close to the point of tangency
The linear approximation at a point is fundamental to understanding derivatives and local behavior of functions.
A aproximação linear em um ponto é fundamental para entender derivadas e o comportamento local de funções.
This is specialized mathematical terminology used in calculus and engineering education across both Brazil and Portugal. In Brazilian universities, it is a core concept taught in Cálculo I (Calculus I) courses. The concept bridges pure mathematics and practical applications in engineering, physics, and economics, making it culturally significant in STEM education in Portuguese-speaking countries.
Related Idioms & Phrases
to approximate a function using linear approximation
linear approximation is accurate in a neighborhood of the point
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