2 n e 2 3 2 3 lim n n n 1 1 1 3 2 lim lim n n n n n 1 1 1 1 5 n e 1 5 1 5 lim n

2 n e 2 3 2 3 lim n n n 1 1 1 3 2 lim lim n n n n n 1

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2 = n e 2 3 2 3 lim n n n 1 1 1 3 2 lim lim n n n n n 1 1 1 1 5 + = + = n e 1 5 1 5 lim n n n 1 1 1 5 + lim n n n 1 1 3 2 lim n n n 1 1 5 + 015
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386 Límite de una función Calcula los límites laterales en el punto x = 3 de: Halla los límites laterales en x = 0 de las funciones. a) b) a) b) Calcula el límite de la función en x = 2 y en x = 5. Razona si existe o no el límite de la función en x = 2, en x = 3 y en x = 4. Halla los siguientes límites. a) b) a) b) lim lim x x x x x x x x + = + + + 2 4 3 2 2 16 8 4 2 2 ( )( )( ) ( 2 2 4 8 3 2 )( ) x x + = − lim x x x + 2 4 3 16 8 0 0 lim lim x x x x x x x x x x x 1 3 2 2 1 2 2 3 2 1 1 + + = ( ) ( )( 2 0 ) = lim x x x x x x 1 3 2 2 2 3 2 0 0 + + lim x x x + 2 4 3 16 8 lim x x x x x x 1 3 2 2 2 3 2 + + 023 lim x f x 4 53 14 ( ) = lim x f x 3 37 6 ( ) = lim lim x x f x f x 2 2 + = − = + ( ) ( ) No existe lim x f x 2 ( ). lim x f x 2 5 0 ( ) f x x x x x ( ) = + + + 2 3 3 2 022 lim lim x x f x f x 5 5 + = − = + ( ) ( ) No existe lim x f x 5 ( ). lim x f x 5 24 0 ( ) lim x f x 2 1 ( ) = − f x x x ( ) = 2 1 5 021 lim x f x 0 1 + = ( ) lim x f x 0 1 = − ( ) f x x x ( ) = > < 1 0 1 0 si si lim x f x 0 + = + ( ) lim x f x 0 = − ( ) f x x x ( ) = ⏐ ⏐ f x x x ( ) = 1 2 020 lim lim x x f x x 3 3 2 1 10 + + = + = ( ) ( ) lim lim x x f x x 3 3 3 0 = = ( ) ( ) f x x x x x ( ) = < + 3 3 1 3 2 si si 019
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387 9 SOLUCIONARIO Calcula si m = 2 y m = 3. ¿Puedes determinar el límite para un valor m cualquiera? Pon un ejemplo de una función que tenga como asíntotas verticales las rectas cuyas ecuaciones son: x = 1 x = 2 x = 3 Respuesta abierta. Por ejemplo: Halla las asíntotas verticales de las funciones. a) b) c) a) Dom f = {0} f ( x ) tiene una asíntota vertical en x = 0. b) Dom f = { 1, 1} f ( x ) tiene una asíntota vertical en x = − 1. f ( x ) tiene una asíntota vertical en x = 1. c) Dom f = { 2, 0, 2} f ( x ) tiene una asíntota vertical en x = − 2. f ( x ) tiene una asíntota vertical en x = 2. f ( x ) tiene una asíntota vertical en x = 0. lim lim x x f x f x 0 0 + = + = − ( ) ( ) lim lim x x f x f x 2 2 + = − = + ( ) ( ) lim lim x x f x f x + = − = + 2 2 ( ) ( ) lim lim x x f x f x 1 1 + = − = + ( ) ( ) lim lim x x f x f x + = + = − 1 1 ( ) ( ) lim lim x x f x f x 0 0 + = − = + ( ) ( ) f x x x ( ) = 1 4 3 f x x ( ) = 1 1 2 f x x ( ) = 1 026 f x x x x ( ) ( )( )( ) = 1
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