LISTA_17 - ıntotas horizontais e verticais do gr´afico...

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Lista 17 alculo I -A- 2007-1 33 Universidade Federal Fluminense EGM - Instituto de Matem´atica GMA - Departamento de Matem´atica Aplicada LISTA 17 - 2007-1 Fun¸ c˜oes hiperb´olicas 1. Se senh x = - 1 4 , encontre: (a) cosh x (b) tanh x (c) senh2 x 2. Determine x tal que tanh x = - 1 4 . Nos exerc´ ıcios 3. a 5. mostre que as igualdades se verificam. 3. tanh(ln x ) = x 2 - 1 x 2 + 1 4. cosh x + senh x = e x 5. (cosh x + senh x ) n = cosh nx + senh nx (sugest˜ao: use o exerc´ ıcio 4.) Derive as fun¸c˜ oes dos exerc´ ıcios 6. a 8. 6. f ( x ) = tanh(sen x ) 7. f ( x ) = senh(ln2 x ) + cosh(ln2 x ) 8. f ( x ) = x cosh x 9. Mostre que cot( π cosh(ln3)) - arcsen (tan( π senh(ln2))) = π 2 - 3 3 . Calcule os limites dos exerc´ ıcios 10. e 11. 10. lim x 0 ± 1 + e x 2 coth x 11. lim x 0+ ± senh x x 1 x 12. Encontre, se existirem, as ass´
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Unformatted text preview: ıntotas horizontais e verticais do gr´afico da fun¸c˜ao f ( x ) = x cosh x e esboce o seu gr´afico. RESPOSTAS 1. (a) √ 17 4 (b)-√ 17 17 (c)-√ 17 8 2. 1 2 ln 3 5 3. tanh(ln x ) = 1 2 ( e ln x-e-ln x ) 1 2 ( e ln x + e-ln x ) = x-1 x x + 1 x = x 2-1 x 2 + 1 4. cosh x + senh x = e x-e-x 2 + e x + e-x 2 = 2 e x 2 = e x 5. cosh nx + sen nx = e nx = ( e x ) n = (cosh x + senh x ) n 6. f ( x ) = cos x sech 2 (sen x ) 7. f ( x ) = 2 8. x cosh x ± senh x ln x + cosh x x ¶ 10. e 1 2 11. 1 12. N˜ao tem ass´ ıntotas y x –2 –1 1 2 lim x →-∞ f ( x ) =-∞ lim x →∞ f ( x ) = ∞...
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