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.
Synonyms / Sinônimos
tangent line approximationlinearizationfirst-order Taylor approximationlocal linear approximation
Antonyms / Antônimos
higher-order approximationnonlinear approximation

Regional Variations

General Brazilian Portuguese
aproximação linear em um ponto
Standard mathematical terminology used in universities and textbooks
Portugal
aproximação linear num ponto
European Portuguese uses 'num' instead of 'em um'; same technical meaning
Academic/International
linearização
Shorter alternative term, commonly used in scientific papers and advanced texts
Educational contexts
reta tangente de aproximação
More descriptive term emphasizing the tangent line aspect

Related Words

tangent linederivativeTaylor seriesdifferentialcalculusapproximation error

Related Idioms & Phrases

to approximate a function using linear approximation
linear approximation is accurate in a neighborhood of the point
Look up more words on Fala2Me
The free English-Portuguese dictionary with real Brazilian accents, NYC slang, conjugator and more
Open Fala2Me →