As regras de L’Hospital podem ser enunciadas da seguinte forma: Sejam f e g deriváveis com limit as x rightwards arrow p of f left parenthesis ...

As regras de L’Hospital podem ser enunciadas da seguinte forma: Sejam f e g deriváveis com limit as x rightwards arrow p of f left parenthesis x right parenthesis equals limit as x rightwards arrow p of g left parenthesis x right parenthesis equals 0, de modo que exista limit as x rightwards arrow p of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction. Então: limit as x rightwards arrow p of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow p of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction . E caso sejam f e g deriváveis com limit as x rightwards arrow p of f left parenthesis x right parenthesis equals limit as x rightwards arrow p of g left parenthesis x right parenthesis equals plus-or-minus infinity , de modo que exista limit as x rightwards arrow p of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction. Então: limit as x rightwards arrow p of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow p of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction . Resuma as informações acima e assinale a alternativa CORRETA. a. As regras de L’Hospital garantem que, se pelo menos um das duas funções for contínua, então existem derivadas, e significa que há um valor de tendência representado pelos limites limit as x rightwards arrow p of begin inline style fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style equals limit as x rightwards arrow p of begin inline style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction end style. b. As regras de L’Hospital garantem que, se as duas funções forem contínuas, então existem derivadas, e significa que há um valor de tendência representado pelos limites limit as x rightwards arrow p of begin inline style fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style equals limit as x rightwards arrow p of begin inline style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction end style. c. As duas regras de L’Hospital garantem que, se pelo menos uma das duas funções for contínua, então existem derivadas, e significa que há um valor de tendência representado pelos limites limit as x rightwards arrow p of begin inline style fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style equals limit as x rightwards arrow p of begin inline style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction end style. d. As regras de L’Hospital garantem que, se as duas funções forem descontínuas, então existem derivadas, e significa que não há um valor de tendência que possa ser representado pelos limites limit as x rightwards arrow p of begin inline style fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style equals limit as x rightwards arrow p of begin inline style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction end style. e. As regras de L’Hospital garantem que, se as duas funções forem contínuas, então não existem derivadas e nem há um valor de tendência que possa ser representado sem o uso de derivadas.