Question

Dado o limx→4(-x+4)=0 e ε=0,02, assinale a alternativa que representa um δ positivo. A. 0,02. B. 0,04. C. 0,06. D. 0,08. E. 0,1.

Answer 1

Resposta:

Letra A

Explicação passo a passo:

$0<|x-a|<\delta\implies|f(x)-L<\epsilon\\\\|-x+4-0|<0,02\\\\|-x+4|<0,02\\\\-0,02<x-4<0,02\\\\4-0,02<x<4 +0,02\\\\3,98<x<4,02~~(I)\\\\De~0<|x-a|<\delta\implies|x-a|<\delta\\\\-\delta<x-4<\delta\\\\4-\delta<x<4+\delta~~(II)\\\\Comparando~~(I)~~e~~(II)\\\\4-\delta=3,98\implies\delta=4-3,98\impies\\\\\delta=0,02\\\\Poderia ~~comparar~~tambem~~4+\delta=4,02\implies\delta=0,02$