Cap 2 (Pot e Rad)

Prévia do material em texto

�PAGE �1�
Potenciação		� PAGE �7�
Potenciação
Definição: Seja a um números real e n um número inteiro maior que 1. Então 
.
Nomenclatura: Na potência, 
 chamaremos a de base e n de expoente.
Exemplos:
�
( 
( 
( 
( 
( 
( 
( 
( 
�
Por definição temos que: 
, 
 e 
.
Logo, 
, 
, 
 e 
.
Importante: Não está definido o símbolo 
 pois este é uma indeterminação.
Propriedades das potências
		Ex.: 
 ou 
		Ex.: 
 ou 
		Ex.: 
 ou 
		Ex.: 
 ou 
		Ex.: 
 ou 
Exercícios em aula:
Calcule:
�
�
Simplifique:
�
�
Resolva:
�
�
Exercícios resolvidos
�
Resolva: 
Solução: 
Resposta: 
Solução:
Resposta: 
Solução: 
	
Resposta: 
Solução: 
	
Resposta: 
Solução:
	
Resposta: 
.
Solução:
	Fazendo 
, vem:
	
	logo 
 não convém!
Resposta: 
Solução:
	Fazendo 
, temos:
	
	
	
Resposta: 
Solução:
	
	Fazendo 
, vem:
Resposta: 
Solução:
	
 1o membro nunca se anula.
Resposta: Não existe solução.
�
Exercícios propostos:
Calcule:
�
�
Calcule: 
�
�
Calcule: 
�
�
Assinale ( V ) ou ( F ):
�
	( )
	( )
	( )
	( )
	( )
	( )
	( )
	( )
�
Simplifique: 
�
�
Resolva as equações:
�
�
Resolva:
�
�
Efetue:
�
�
�
Radiciação
Definição:	( Para n inteiro positivo ímpar 
		( Para n inteiro positivo par 
Exemplos:	( 
		( 
		( 
		( 
		( 
		( 
		( 
		( 
 (falso!)
		( 
		( 
	(
		( 
 (falso!)
		( 
		( 
		( 
		( 
 (falso!)
Nomenclatura: Na raiz 
 chamamos n de índice do radical e a de radicando.
Propriedades: Sejam 
.
		Exemplo: 
			Exemplo: 
		Exemplo: 
		Exemplo: 
		Exemplo: 
Importante: As propriedades listadas acima só valem para o caso do radicando ser maior ou igual a zero. Se o radicando for negativo, o uso das propriedades acima pode nos levar a contradições. Por exemplo: 
, (- 2 = 2 ???? )
Potência de expoente racional: 
 onde a é não negativo e n é inteiro positivo.
Exercícios em aula
Calcule:
�
�
�
Racionalize:
�
�
Sendo 
, calcule:
�
 
�
Resolva:
�
�
Exercícios resolvidos
Racionalize:
�
Solução: 
	
Resposta: 
Solução:
	
Resposta: 
�
Solução:
	
Resposta:
Solução:
	
Resposta: 
Solução:
	
Resposta: 
Coloque em ordem crescente os números 
.
Solução:
 	Comparamos radicais, reduzindo-os ao mesmo índice. O índice comum é o m.m.c. dos índices dados. Neste caso, o índice comum é 12 = mmc (2, 3, 4). Temos então:
 		
 		
 
 		
 	Como 
, temos que 
.
 	Resposta: 
.
Se 
 calcule 
.
Solução:
	
	
	
	
	
	
	
Resposta: 110.
Exercícios propostos
Use as propriedades de potência para provar as propriedades de radiciação.
Assinale (V) ou (F):
�
	( )
	( )
	( )
	( )
 		( )
	( )
	( )
		( )
	( )
	( )
	( )
	( )
	( )
	( )
		( )
		( )
		( )
			( )�
Racionalize:
�
�
�
�
Simplifique:
�
�
�
Simplifique: 
 sabendo que 
.
Sabendo que 
, simplifique 
.
Calcule:
�
�
Efetue:
�
.
.
�
Qual a ordem crescente dos números 
?
�
�
Coloque os seguintes números em ordem decrescente: 
Resolva:
�
�
Se 
 calcule 
.
Se 
 calcule 
.
Se 
 calcule 
.
Se 
 calcule 
.
Se 
 calcule:
�
�
Sendo 
, obtenha:
�
 
.
�
Sabendo que 
, calcule o valor de 
.
Resolva o sistema 
.
Reforço: Ver também [ B, pág.76 ], [ I2], [ Ma, pág. 157] e [ Me, pág.20].
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