Question
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  1. Considera a função real de variável real definida por:
8.1. Calcula .
8.2. Determina as coordenadas dos pontos de intersȩ̧ăo do gráico de com os exxos coordenados.

Ask by Moreno Wheeler. in Portugal
Jan 23,2025

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Answer

8.1. Cálculo de :
  • Resultado:
8.2. Coordenadas dos pontos de interseção do gráfico de com os eixos coordenados:
  • Eixo :
  • Eixo : , , e

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Para resolver a questão:
8.1. Vamos calcular , e usando as definições da função:
  • Para (onde ):
    .
  • Para (onde ):
    .
  • Para (onde ):
    .
Assim, .
8.2. Para encontrar as coordenadas dos pontos de interseção do gráfico de com os eixos coordenados, vamos verificar onde :
  1. Para , temos .
  2. Para , temos , então e (considerando ).
  3. Para , temos .
Portanto, os pontos de interseção com os eixos coordenados são:
  • Com o eixo : , , , e .
  • Com o eixo : Para isso, calculamos , portanto, o ponto é .

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