inecuaciones - puntos críticos

GRUPO EDUCATIVO AVANTGARD

SEDE SUPERIORSEDE SUPERIORSEDE SUPERIORSEDE SUPERIOR JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN

01. Resolver: (x + 3) (x – 5) (x – 1) < 0

A) ⟨–∞, –3⟩ ∪ ⟨1, 5⟩

B) ⟨–∞, –3] ∪ [1, 5⟩

C) ⟨–∞, 1⟩ ∪ ⟨3, 5⟩

D) ⟨–∞, 1⟩ ∪ [3, 5⟩

E) N.A.

02. Resolver: (x – 1) (x – 4) (x + 7) > 0

A) ⟨–7, 1⟩ ∪ [4, +∞⟩ B) ⟨–1, 0] ∪ [4, +∞⟩ C) ⟨–7, 1⟩ ∪ ⟨4, +∞⟩ D) ⟨–1, 4⟩ ∪ [7, +∞⟩ E) N.A.

03. Resolver: (x + 2) (x – 1) (x – 3) (x + 5)

A) ⟨–5, –2⟩ ∪ ⟨1, 3⟩

B) ⟨–∞, –5] ∪ ⟨–2, 1⟩

C) ⟨–∞, –5⟩ ∪ ⟨–2, 1⟩ ∪ ⟨1, +∞⟩ D) [–5, –2] ∪ [1, 3]

E) N.A.

04. Resolver: 0)2x()2x(

)5x()1x()x3(≥

−+−+−

A) ⟨–2, –1] ∪ ⟨2, 3⟩ ∪ [5, +∞⟩ B) ⟨–∞, –2] ∪ [–1, 2] ∪ [ 3, 5 ]

C) ⟨–∞, –2⟩ ∪ [–1, 2⟩ ∪ [ 3, 5 ]

D) [–2, –1] ∪ [2, 3]

E) N.A.

05. Resolver: x2 – 7x + 10 ≤ 0

A) x ∈ ⟨–∞, 2⟩ ∪ ⟨5, +∞⟩ B) x ∈ [2, 5]

C) x ∈ [5, +∞⟩ D) x ∈ ⟨∞, 2⟩

E) N.A.

06. Resolver: x2 + 4x – 45 > 0

A) x ∈ ⟨–∞, –9⟩ ∪ ⟨5, +∞⟩ B) x ∈ ⟨–∞, –15⟩ ∪ ⟨3, +∞⟩ C) x ∈ [–9, 5]

D) x ∈ [–15, 3⟩

E) N.A.

JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN

1) < 0

4) (x + 7) > 0

3) (x + 5) ≤ 0

07. Resolver: x2 – 13x + 30 < 0

A) ⟨2, 15⟩ C)

B) ⟨3, 12⟩ D)

08. Resolver: x2 – 3x + 2

A) ⟨–∞, 1⟩ C) [2, +

B) ⟨2, +∞⟩ D)

09. Resolver: x2 + 4x + 11 < 0

A) ⟨1, 3⟩ C)

B) ℜ D)

10. Resolver: 2x2 + x –

A) ⟨–1, 2

1⟩ C)

B) ⟨–1, 5⟩ D)

11. Resolver: x

()x24( −

A) [–1, 0] ∪ [2, +∞[

C) ]–1, 0] ∪ [2, +∞[

B) ]–1, 0[ ∪ ]2, +∞[

D) φ

E) N.A.

12. Resolver: 2x

8x

+−

< 0

A) x ∈ ⟨–3, 4]

B) x ∈ ⟨–2, 8⟩

C) x ∈ ⟨–∞, 2⟩ ∪ ⟨8, +

D) x ∈ ⟨–∞, 3⟩ ∪ ⟨5, +

E) N.A.

13. Resolver: 1x

9x

−+

≥ 0

A) x ∈ ⟨–∞, 6] ∪ ⟨1, +

B) x ∈ ⟨–∞, –6⟩ ∪ ⟨2, +

C) x ∈ ⟨–∞, –9] ∪ ⟨1, +

D) x ∈ ⟨–9, 1⟩

E) N.A.

INECUACIONES - FUNCIONES

JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN 1111

13x + 30 < 0

C) ⟨3, 10⟩ E) ⟨7, 10⟩

D) ⟨2, 7⟩

3x + 2 ≥ 0

C) [2, +∞⟩ E) ⟨3, +∞⟩ D) ⟨–∞, 1] ∪ [2, +∞⟩

+ 4x + 11 < 0

C) ⟨–∞, 1⟩ E) φ

D) ⟨2, +∞⟩

– 1 < 0

C) ⟨–2, 2

1⟩ E) ⟨1, 7⟩

D) ⟨–1, 3

1⟩

)1x( + ≤ 0

< 0

8, +∞⟩ 5, +∞⟩

1, +∞⟩ 2, +∞⟩ 1, +∞⟩

FUNCIONES

GRUPO EDUCATIVO AVANTGARD

SEDE SUPERIORSEDE SUPERIORSEDE SUPERIORSEDE SUPERIOR JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN

14. Resolver: )2x(x

)5x()3x(

+−+

≥ 0*

A) ]–∞, –3] ∪ [5, +∞[

B) ]–∞, –3] ∪ ]–2, 0[ ∪ ]5, +∞[

C) ]–∞, –3[ ∪ ]–2, 0[ ∪ ]5, +∞[

D) ]–∞, –3] ∪ ]–2, 0[ ∪ [5, +∞[

E) ]–2, 0[ ∪ ]5, +∞[

15. Resolver: )3x()1x(

)2x(x

−+−

> 0

A) ]–∞, –1[ ∪ ]0, 2[ ∪ ]3, +∞[

B) ]–∞, –1] ∪ [0, 2] ∪ [3, +∞[

C) ]–∞, –1[ ∪ ]0, 2[ ∪ [3, +∞[

D) ]–∞, –1[ ∪ ]3, +∞[

E) N.A.

16. Resolver: 21x

2x<

−+

A) ]4, + ∞[ C) ]1, + ∞[ E) ]

B) ]–∞, 1[ D) ]–∞, 1[ ∪ ]4, +

17. Resolver: 5

x

2x

1

5

1x>

+−

+

A) ]–2, 3[

B) ]3, +∞[

C) ]–∞, –2[

D) ]–∞, –2[ ∪ ]3, +∞[

E) ]–∞, 3[

18. Resolver: 3x2 – 10x ≤ – 3

A) ⟨1/3, 3⟩ C) φ E) N.A.

B) [1/3, 3] D) ⟨–∞, 3⟩

19. Resolver: x (6x + 17) > 3

A) ⟨–∞, –3⟩ ∪ ⟨1/6, +∞⟩

B) ⟨–∞, –3] ∪ [1/6, +∞⟩ C) ⟨–∞, –1/6⟩ ∪ ⟨3, +∞⟩ D) ⟨–∞, 1/6⟩ ∪ [3, +∞⟩ E) N.A.

20. Resolver: 8 + 2x – x2 ≥ 0

A) [–2, 4] C) ] –2, 4[ E) N.A.

B) [–2, 4[ D) ] –2, 4]

JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN

E) ]–∞, 4[

]4, + ∞[

E) N.A.

E) N.A.

21. Resolver: x2 + 4x + 4 < 0

A) ]–∞, –2[ C) ]

B) ]–∞, –2] D) ]

22. Resolver: x2 + x + 1 > 0

A) φ B) ℜ

D) +1 E) N.A.

23. Resolver: x2 – 4x > 12 y dar como

respuesta un intervalo

A) ]– ∞, –2[ C) ]

B) [2, +∞] D) [

24. Resolver: x (x + 5)

A) ⟨–∞, –4⟩ C)

B) ⟨–4, +∞⟩ D)

25. Resolver: x)x2(

x()x2(

−+−

A) ⟨0, –1⟩ C)

B) ⟨–1, 0] D) [

26. Resolver: x4x

2()x5(2 −−

+−

A) ⟨–∞, –2] ∪ ⟨–1, +∞⟩B) ⟨–∞, –2] ∪ ⟨–1, +∞⟩C) [–2,– 1]

D) [–1, +∞⟩ – {5}

E) ⟨–∞, –2⟩ ∪ ⟨–1, +∞⟩

27. Resolver: x

x

3x

9x

+−≤

−−

A) [–3, –1] ∪ [3, +∞⟩ B) [–3, –1] ∪ ⟨3, +∞⟩ C) ℜ – {3, 1}

28. Resolver: 6xx

2x2 −+

+

A) ⟨–3, –2⟩ ∪ ⟨2, +∞⟩ B) ⟨2, +∞⟩ C) ⟨3, +∞⟩

29. Resolver: 1x

14x5x2

2

−

−+

A) ⟨–7, –1⟩

B) ⟨1, 2⟩

C) ℜ

JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN JOHN CARLOS VÁSQUEZ HUAMÁN 2222

+ 4x + 4 < 0

C) ]–∞, 2[ E) φ

D) ]–2, +∞[

+ x + 1 > 0

C) –1

4x > 12 y dar como

C) ] –∞, 6[ E) N.A.

D) [–6, +∞]

x (x + 5) ≤ – 4

C) ⟨–1, +∞⟩ E) [–4, –1]

φ

)1 < 0

C) ⟨–1, 0⟩ E) N.A.

D) [–1, 0]

5

)x ≤ 0

⟩

⟩ – {5}

⟩ – {5}

1

1

+−

D) φ

E) N.A.

0>

D) ⟨–∞, –1⟩

E) ℜ

014

≤

D) ⟨–7, –1⟩ ∪ ⟨1, 2⟩

E) [–7, –1⟩ ∪ ⟨1, 2]