tangent line approximation
[/ˈtændʒənt laɪn əˈprɑːksɪˌmeɪʃən/]
nounpl: tangent line approximations
aproximação pela reta tangente
1. A method in calculus that uses the tangent line to a curve at a given point to approximate the value of the function at nearby points
The tangent line approximation gives us f(x) ≈ f(a) + f'(a)(x - a) near the point x = a
A aproximação pela reta tangente nos fornece f(x) ≈ f(a) + f'(a)(x - a) próximo ao ponto x = a
2. The linear approximation of a function using the derivative at a specific point
We used tangent line approximation to estimate √4.1 without a calculator
Usamos a aproximação pela reta tangente para estimar √4,1 sem calculadora
This is a fundamental concept in calculus taught in secondary and higher education in both Brazil and the USA. In Brazilian universities, it's commonly presented as 'aproximação linear' or 'aproximação pela reta tangente' in calculus courses (Cálculo I). The concept is essential for understanding differential calculus and numerical methods. In Portugal, the terminology uses 'recta' (straight line) rather than 'reta', following European Portuguese conventions.
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