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Clase 111

Clase 111. 9 x. 2. Ejercicios sobre ecuaciones e inecuaciones exponenciales. =. >. (4 x ) x. 2 8 x +6. 3 3 x –1. Estudio individual de la clase anterior. 4. x 3 + 4 x 2 – 20. f ( x ) =. + 4. x + 5.  .

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Clase 111

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  1. Clase 111 9x 2 Ejercicios sobre ecuaciones e inecuaciones exponenciales = > (4x)x 28x+6 33x–1

  2. Estudio individual de la clase anterior. 4 x3+ 4x2 – 20 f (x) = + 4 x + 5  1.Halla el dominio de definición de la función f , dada por la ecuación Domf: x0 ; x  –5 ; x = –2

  3. x3+ 4x2– 20 + 4  0 x + 5 x3+ 4x2 – 20 + 4 x + 5  x3+ 4x2–20 + 4x + 20  0 x +5 4 f (x) = + 4(x + 5) x3+ 4x2–20  0 x +5

  4. x(x2+ 4x + 4)  0 x +5 x(x + 2)2  0 x +5 –5 –2 0 x3+ 4x2+ 4x C.N. x1= 0  0 x +5 x2= – 2 doble x3= – 5 C.D. + + Domf: x 0 ; x  –5 ; x = –2

  5. 7x(x+1) (73+x)3–x  b) 1 x+4 76 x x+1 25 · 5 = 125 Ejercicio 1 Para qué valores de x se cumple: a)

  6. (52) · 5 = 53 5 · 5 = 53 2 1 2 2 1 x+4 x+4 x+4 x+4 x+4 x x x x x x+1 x+1 x+1 x+1 x+1 25 · 5 = 125 + 5 = 53 = 3 + a) Dominio: x : x  0; x  – 1

  7. 2 x+4 · x(x+1) x x+1 1 x1= – = 3 + 2 Dominio: x : x  0; x  – 1 2(x+1) + x(x+4) = 3x(x+1) + x2+4x 2x + 2 = 3x2+3x 2x2 – 3x – 2 = 0 (2x + 1)(x – 2) = 0 ó x2 = 2

  8. 7x(x+1) (73+x)3–x  b) 76 2 79– x 7x(x+1) – 6  9 – x2x(x+1) – 6 9 – x2x2+ x – 6 2x2 + x – 150

  9. 5 x1= 2,5 –3 2 2x2 + x – 150 Ceros 2x2 + x – 15=0 (2x – 5)(x + 3) = 0 ó x + 3= 0 2x – 5 = 0 x2= –3 x1= 2,5 + + x   ; –3  x  2,5

  10. x – 1 4 · 2 = 16  x – 8 1 3 1 x+1 x+2 x+3 > · 9 3 3 Para el estudio individual Para qué valores de x se cumple: a) Resp: N.S b) Resp: –3<x< –2 ó –1<x< 1

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