inecuaciones - puntos críticos
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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]