(0, 2 - 0, 12) / 0, 1

Passo 1

Beleza, vamos dar uma olhada nesse exercício juntos! A gente precisa resolver a expressão . Aqui, estamos lidando com números decimais periódicos, que é um tópico de Matemática envolvendo frações e decimais que se repetem infinitamente. Para resolver isso, vamos transformar esses decimais em frações e depois simplificar a expressão.

Passo 2

Primeiro, vamos transformar cada número decimal periódico em fração. Vamos começar com . Esse número significa que se repete infinitamente. A forma geral para converter um decimal periódico simples como esse em fração é:
y = sen(x^2)
Então, para y = sen(x^2) temos:

Passo 3

Agora, vamos converter . Esse número é repetindo infinitamente. Para decimais com dois dígitos que se repetem, a fórmula é:
y = sen(x^2)
Onde “ab” são os dígitos que se repetem. Então, para y = sen(x^2):
Podemos simplificar essa fração dividindo numerador e denominador por 3:
y = sen(x^2)

Passo 4

Vamos também converter o denominador . Esse é repetindo. Usando a mesma fórmula de um dígito que se repete:
y = sen(x^2)

Passo 5

Agora que temos todas as partes convertidas em frações, vamos substituir na expressão original:
y = sen(x^2)

Passo 6

Vamos resolver o numerador primeiro: . Para subtrair essas frações, precisamos de um denominador comum. O menor múltiplo comum entre 9 e 33 é 99. Então, ajustamos as frações:
y = sen(x^2)
y = sen(x^2)
Agora, subtraímos:
y = sen(x^2)

Passo 7

Agora temos:
y = sen(x^2)
Dividir frações é o mesmo que multiplicar pela inversa. Então:
y = sen(x^2)
Podemos simplificar y = sen(x^2) dividindo numerador e denominador por 9:
y = sen(x^2)

Resposta

A expressão simplifica para .

Exercícios relacionados

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Esboce o gráfico de uma função que seja contínua exceto para a descontinuidade declarada.
c) Descontinuidade removivel em 3 .
<html><head></head><body><div>(b) Para cada um dos números indicados na parte (a), determine se <span class="math-inline " data-overflow=“visible”>
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