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gma00108-lista-05 - DEPARTAMENTO DE MATEMTICA APLICADA GMA...

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GMA DEPARTAMENTO DE MATEMÁTICA APLICADA LISTA DE EXERC ´ ICIOS alculo I –A– Humberto Jos´ e Bortolossi http://www.professores.uff.br/hjbortol/ 05 Opera¸c˜ oes com limites, o teorema do confronto e o teorema do anulamento [01] Os gr´ aficos das fun¸ c˜oes f e g s˜ao dados abaixo. Use-os pra calcular cada limite, caso ele exista. (a) lim x 2 [ f ( x ) + g ( x )], (b) lim x 1 [ f ( x ) + g ( x )], (c) lim x 0 [ f ( x ) · g ( x )], (d) lim x →− 1 g ( x ) f ( x ) , (e) lim x 2 [ x 3 · f ( x )], (f) lim x 1 3 + f ( x ). . [02] Considere as fun¸ c˜oes f ( x ) = x 2 + x 6 x 2 e g ( x ) = x + 3 . (a) As fun¸ c˜oes f e g s˜ao diferentes. Por quˆ e? (b) Apesar de f e g serem diferentes, ainda ´ e verdade que lim x 2 x 2 + x 6 x 2 = lim x 2 ( x + 3) . Por quˆ e? [03] Calcule cada limite abaixo, se ele existir. (a) lim t 0 2 t 2 t , (b) lim x 2 x 4 16 x 2 , (c) lim x 9 x 2 81 x 3 , (c) lim x 1 x x 2 1 x . [04] Uma fun¸ c˜ao f : R R satisfaz a seguinte propriedade: 1 + 4 x x 2 f ( x ) x 2 4 x + 9 para
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