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LISTA_04 - Lista 4 Clculo I-Aa 2007-1 7 Universidade...

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Lista 4 alculo I -A- 2007-1 7 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 4 - 2007-1 Limite infinito e no infinito Teoremas do confronto e anulamento Limites trigonom´ etricos Nos exerc´ ıcios 1. a 4. os gr´aficos de g e h s˜ao dados. Ache os limites laterais de f no ponto indicado. 1. f ( x ) = g ( x ) h ( x ) , no ponto x = 2 h g y x –2 0 2 4 –2 2 4 6 8 2. f ( x ) = g ( x ) h ( x ) , no ponto x = 3 g y x –2 2 4 –3 –2 –1 1 2 3 4 5 6 7 8 h y x –100 0 100 200 300 –2 2 4 6 8 3. f ( x ) = g ( x ) h ( x ) , no ponto x = 2 g y x –1 1 2 3 4 5 6 –2 2 4 h y x –300 –200 –100 0 100 200 300 –2 2 4 6 8 4. f ( x ) = g ( x ) h ( x ) e f ( x ) = ( g h )( x ) ambas no ponto x = 4 h g y x –2 2 4 6 8 –2 2 4 6 8 Nos exercic´ ıos 5. a 10. calcule o limite, caso exista. Caso n˜ao exista, justifique. 5. lim x + ( x n - x n - 1 ) 6. lim x + ( x + 1)( x + 2) · · · ( x + 10) ( x 2 + 1) 5 7. lim x →-∞ x 2 - 2 x + 2 x + 1 8. lim x →-∞ x + p x 2 + 3 x + 2 · 9. lim x →- 1 3 x + 1 - 5 x 2 - 1 10. lim x 5 ˆ 25 - x 2 x - 5 !
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