# LISTA_03 - Lista 3 de Clculo Aplicado I e Clculo...

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Lista 3 de alculo Aplicado I e C´ alculo Diferencial e Integral Aplicado I 2006-2 5 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 3 - 2006-2 Limite e limites laterais Continuidade 1. Os gr´aficos de g e h ao dados. Ache os limites laterais de f no ponto indicado. f ( x ) = g ( x ) · h ( x ) e f ( x ) = ( h g )( x ) ambas no ponto x = 1 g y x –1 0 1 2 3 4 5 –3 –2 –1 1 2 3 4 h y x –2 2 4 –3 –2 –1 1 2 3 4 2. Dadas as fun¸c˜ oes f ( x ) = x 2 + 3 se x 1 x + 1 se x > 1 e g ( x ) = x 2 se x 1 2 se x > 1 , (i) Esboce o gr´afico de f e g ; (ii) Calcule lim x 1 f ( x ) e lim x 1 g ( x ); (iii) Dˆ e a express˜ao da fun¸c˜ ao F ( x ) = f ( x ) · g ( x ) e verifique se existe lim x 1 F ( x ). 3. Dˆ e um exemplo no qual lim x 0 | f ( x ) | existe, mas lim x 0 f ( x ) n˜ao existe. 4. Se f ( x ) > 0 para todo x 6 = 2 e f (2) = - 3, verifique se as afirmativas abaixo s˜ao verdadeiras ou falsas. Caso seja verdadeira, apresente uma justificativa. Caso seja falsa, apresente um contra-exemplo.

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