Limites

I. Demuestre cada uno de los siguientes límites:
1) Lim 7 = 7
X 2

2) Lim (2x+1)=9
X 4
= Lim 2x + Lim 1 = 2 Lim x + Lim x = 2(4) + 1 = 8 + 1 = 9

3) Lim (4x+3)=7
X 1
= Lim 4x+ Lim 3= 4 Lim x + Lim 3= 4(1) + 3 = 4(1) + 3= 4+3= 7

4) Lim (2x+7)=-1
X -4
= Lim 2x + Lim 7= 2 Lim x + Lim 7= 2(-4) +7 = -8+7= -1

5) Lim (1+3x)=-5
X -2
= Lim 1+ Lim 3x = Lim 1 +3Lim x = 1 + 3(-2) = 1 – 6 = -5

6) Lim (x2-3x)=10
X 5
= Lim x2 – Lim 3x = Lim 52 – 3 Lim x = 25 – 3(5) = 25 -15 =10

7) Lim (4-x)=8
X -4
=Lim 4 – Lim x = Lim 4 – Lim x = 4 – 1(-4) =4+4 = 8

8) Lim (5-x-x2)=-1
X -3
= Lim 5 – Lim x – Lim x2 = 5 – (-3) – (-3)2 = 5+3-9= 8 -9 = -1

9) Lim 2 = 1
X+2 3
X 4
= 2 = 2 = 1
4+2 6 3

10) Lim2 = 2
X-4
X 5
= 2 = 2 = 2
5-4 1

11) Lim √(x + 5) = 3
X 4
√ (4+5) = √9 = 3

12) Lim 1 = 1
√ (3-2x) 3
X -3
1 =1 = 1 = 1
√ [3-2(-3)] √ (3+6) √9 3

13) Lim 4 = 2
X-1
X 3
4 = 4 = 2
3-1 2

14) Lim (3+2x-x2)= 0
X -1
= 3+ 2(-1) - (-12)= 3-2-1= 015) Lim 3x = 3
3x+2 2
X -2
3(-2) = -6 = 3
3(-2)+2 -4 2

16) Lim 1 = -1
X+3
X -4
1 = 1 = -1
(-4)+3 -1

17) Lim √x =2X 4
= √4 = 2

18) Lim 1 = 1
X 2
X 2

19) Lim 1 = 1
X+1 3
X 2
1 = 1
2+1 3

20) Lim 9x2-1 = 0
3x+1
X 1/3
=9(1/3)2-1 = 9(1/9)-1 = 1-1 = 0 = 0
3(1/3)+1 3(1/3)+1 1+1 2

21) Lim √x =1
X 1
= √1 = 1

22) Lim (3-4x)=7
X -1
=3 – 4(-1) = 7
=3+4 = 7

23) Lim x3 =-a3
X -a= -a3

24) Lim 8 = 2
X-3
X 7
= 8 = 8 = 2
7-3 4

II. Encuentre el límite usando límites laterales:

1) Lim(3x – 7)
X 5
= Lim...