LÍMITES DETERMINADOS E INDETERMINADOS
1. lim 5 x3−4 x2+2x+3=¿
x→1
2. lim (5x3−4 x2+1 ) (4 x−7 )=¿x→2
3. lim (x2−3x+2 ) ( x−3 )=¿x→3
4. lim 5( x+3 )3
=
x→−3
5. lim 4 x3−2x2−16 x3+5 x+2
=¿
x→∞
6. lim 9x2
=¿
x→∞
7. lim x2−25x+5
=¿
x→−5
8. lim x2+ x−6x+2
=¿
x→−2
9. lim x2−7 x+2x−5
=¿
x→5
10. limy3+1y+1
=¿
x→1
11. lim T2+T−12T−3
=¿
T→3
12. lim √2+T−√2T
=¿
T→0
13. lim tan θsenθ
=¿
θ→0
14. lim 6 y2−24 y+243 y−6
=¿
y→2
15. Si f ( x )=x2calcular
lim f ( x+h )−f (x)
hh→0
16. Si f ( x )=x2+5 x−3calcular
lim f ( x+h )−f (x)
hh→0
17. lim √x+2−√2x
x→0
18. lim √ 2 x2+3 x+4x3+1x→2
19. lim √ y2−92 y2+7 y+3
y→−3
20. lim √ 8T 3−2T4 T2−1
T→ 32
21. lim 2−√4−TT
=¿
T→0
22. lim x2−813−√ x
=¿
x→9
23. lim √ 2+5 x−3 x3x2−1=¿
x→3
24. lim V 2 (3V−4 ) (9−V 3 )=¿V →3
25. lim (x2−1 )=¿¿x→1
26. lim 4 x2=¿x→−1
27. lim x3=¿x→−2
28. lim 2 x+7x+7
=¿
x→4
29. lim x2+34
=¿
x→3
30. lim 4 x3−22 x+1
=¿
x→2
31. lim 5x2−4 x+6=¿x→1
32. lim 6 x3−4 x2+1=¿x→−133. lim 4 x2−8 x+5=¿
x→ 12
34. lim 7x3−4 x2+x−9=¿x→3
35. lim 3( x−3 )2
=¿
x→0
36. lim 1x2
=¿
x→0
37. lim 5x=¿
x→∞
38. lim 7x
x→−∞
39. lim x2+4 x+1x+3
=¿
x→∞
40. lim x8
x+4=¿
x→−4
41. lim x+3x2+4 x+1
=¿
x→∞
42. lim 4 x3+2 x−26 x2+5 x+1
=¿
x→∞
43. lim ax2+bx+c
dx3+cx+f=¿
x→∞
44. lim 2x 4+ x2+36 x3+x2−4 x
=¿
x→0
45. lim 8 xx
=¿
x→0
46. lim 6 x2−3 x+14 x+2
=¿
x→0
47. lim 5 x4−6x2+2
=¿
x→0
48. lim 6 x3−4 x2+1=¿x→−1
49. lim (x¿¿2−ax)=¿¿x→a
50. lim (−1x2 )=¿
x→0
51. lim 4 h2−62h3+3h2
=¿
h→0
52. lim x2−1x−1
=¿
x→1
53. lim ( x+a ) (2 x+b )x+a
=¿
x→a
54. lim ¿¿¿T→−1
55. lim ¿¿h→0
56. lim (3 x¿¿3¿−2 x2− x+7)=¿¿¿x→2
57. lim √ 9 x2+3 x−9x2+3=¿
x→1
58. lim x−3x2−9
=¿
x→3
59. lim ¿¿¿x→0
60. lim x2−2 xx
=¿
x→0
61. lim x3−8x−2
=¿
x→2
62. lim
1x2– 2x+3
1x3
+5=¿
x→0
63. lim 1x ( 13+x
−13 )=¿
x→0
64. lim x+21−√2 x+5
=¿
x→−2
65. lim √ x+h−√xh
=¿
h→066. lim 2x−62−√3 x−5
=¿
x→3
67. lim (−3 )=¿x→1
68. lim √7=¿x→−3
69. lim (8+ 35 x )=¿
x→−2
70. lim 27x−3
x→7
71. lim x4+x2−1x6−2
=¿
x→−1
72. lim 3√8 x2−x+3=¿x→2
73. lim √ x4+1x2+1=¿
x→1
74. lim √ x+412
=¿
x→5
75. lim x2−5 x−6x−6
=¿
x→6
76. lim x−3x2−9
=¿
x→3
77. lim 4 x3−2x2
4 x2−2x3=¿
x→078. lim x3+27x+3
=¿
x→−3
79. lim ¿¿¿h→0
80. lim h1h
=¿¿
h→0
81. lim ¿¿¿h→0
82. lim
1x2– 3x+51
1x3
−7=¿
x→0
83. lim x+13−√x+10
=¿
x→−1
84. lim x+23−√2x+5
=¿
x→2
85. lim √ x+h−√xh
=¿
h→0
86. lim 5 x2−2x+1x2−x+3
=¿
x→∞
87. lim 3 x2−5 x+3x2+ x−1
=¿
x→−∞
88. lim 3 x2−1
x3+12=¿
x→∞
89. lim 8 x2+5
x3+5=¿
x→−∞
90. lim x2−2 x+58 x3+x+2
=¿
x→∞
91. lim x2−9x+5
=¿
x→−∞
92. lim 4 x2+32 x2−1
=¿
x→∞
93. lim √x2−1−xx→∞
94. lim x2
x+5=¿
x→∞
95. lim 3 x−x2
4 x+5=¿
x→∞
96. lim xx+3
=¿
x→−3
97. lim x+2x2−4
=¿
x→∞
98. lim −5 x4+9x4−1
=¿
x→∞
99. lim √ x2+4x+4
=¿
x→∞
100. lim √ x2+5x+5
=¿
x→−∞
101. lim 3 x−1√8 x2−9
=¿
x→−∞
102. lim √ y2+7y−1
=¿
y→∞
103. lim 2 x+3√ x2−1
=¿
x→−∞
104. lim √x2+1−xx→∞
105. lim 3 x3+5 x2−710 x3−11 x2+5 x
=¿
x→0
106. lim 4 x+52x+3
=¿
x→∞
107. lim 4T2+3T+2T 3+2T−6
=¿
T→0
108. lim 4 y2−32 y3+3 y2
=¿
y→∞
109. lim 6 x3−5 x2+32 x3+4 x−7
=¿
x→∞110. lim s4−a4
s2−a2=¿
s→a
111. lim √ x+h−√xh
=¿
h→0
112. Si f ( x )=1xcalcular
lim f ( x+h )−f (x)
hh→0
113. Si f ( x )=x3 calcular
lim f ( x+h )− f (x)
hh→0
114. lim (x3−5 x2+2 x−1 )=¿x→3
115. lim x2−9x+3
=¿
x→−3
116. lim 1x+1
+1
x+2=¿
x→−2
117. lim x2−4x−2
=¿
x→2
118. lim 1x– 13
x−3=¿
x→3
119. lim 1x+2
−15
x−3=¿
x→3
120. lim 1√x
−12
x−4=¿
x→4
121. lim 15+h
−15
h=¿
h→0
122. lim z−1z2−1
=¿
z→1
123. lim ¿¿¿h→0
124. lim √ x+3−2x−1
=¿
x→1
125. lim 1x−12
x−2=¿
x→2
126. lim 1z2
−1
z+1=¿
z→−1
127. lim √ x2+1−1x
=¿
x→0
128. lim y+1y−1
– 32
y−5=¿
y→5
129. lim 1x2+1
− 1a2+1
x−a=¿
x→a
130. lim yb2
−b4
y2
y−b2=¿
y→b2
131. lim ¿¿¿h→0
132. lim x3−1x−1
=¿
x→1
133. lim ¿¿¿h→0
134. Si f ( x )=x2−2 x+3calcular
lim f ( x )−f (1)x−1
x→1
135. Si g ( x )=√25−x2 calcular
lim g ( x )−g(4)x−4
x→4
136. lim 9 x2−13x−1=¿
x→ 13
137. lim (5−x−x2 )=¿x→−3
138. lim 3+2 x5−x=¿
x→ 12
139. lim √ x3+2x+3x2+5=¿¿
x→2
140. lim T 2−52T3+6
=¿
T→2
141. lim y3+8y+2
=¿
y→−2
142. lim √ 8 r+1r+3=¿¿
r→1
143. lim √ y2−92 y2+7 y+3
=¿¿
y→−3
144. lim 2 x2−x+54 x3−1
=¿
x→∞
145. lim 4√3 x−5=¿x→7
146. lim √x+1√4 x−1
=¿
x→∞
147. lim ( 1x +1)(5 x2−1x2 )=¿
x→∞
148. lim 3 x2
9−x2=¿
x→3
149. lim x+2x2−4
=¿
x→2
150. lim √ x2+4x
=¿
x→0
151. lim 3 x2−9x+1=¿
x→∞
RESPUESTAS
(1) 34
(2) 25(3)−100(4)∞
(5) 23
(6)0(7)−10(8)∞(9)∞(10) 3
(11) 7
(12) √24
(13) secθ
(14) 0
(15) 2 x
(16) 2 x+5
(17) √24
(18) √2
(19) √ 65(20) √3
(21) 14
(22) −108
(23) −¿2(24) −810
(25) 0
(26) 4
(27) 8
(28) 1511
(29) 3
(30) 6
(31) 7
(32) −9
(33) 2
(34) 147
(35) 13
(36) ∞
(37) 0
(38) 0
(39) ∞
(40) ∞
(41) 0
(42) ∞
(43) 0
(44) ∞
(45) 8
(46) 12
(47) −3
(48) −¿9(49) 0
(50) −∞
(51) −∞
(52) 2
(53) 2a+b
(54) −64
(55) −14
(56) 21
(57) √32
(58) 16
(59) 23
(60) −2
(61) 12
(62) 0
(63) −19
(64) −¿1
(65) +√x2 x
(66) −83
(67) −¿3(68) √7
(69) 345
(70) −1
(71) −1
(72) 3√33
(73) 1
(74) 14
(75) 7
(76) 16
(77) −12
(78) 27
(79) 23
(80) 0
(81) 1
(82) 0
(83) −6
(84) −¿3
(85) √x2x
(86) 5
(87) 3
(88) 0
(89) 0
(90) 0
(91) ∞
(92) 2
(93) ∞
(94) ∞
(95) −∞
(96) −∞
(97) 0
(98) −5
(99) 1
(100) 1
(101) 3√88
(102) 1
(103) 2
(104) ∞
(105) 310
(106) 2
(107) −13
(108) 0
(109) 3
(110) 2a2
(111) √x2x
(112) 2ax+b
(113) 3 x2
(114) −13
(115) −6
(116) −1
(117) 4
(118) −19
(119) −125
(120) −116
(121) −125
(122) 12
(123) 2a
(124) 0
(125) −14
(126) 2
(127) 0
(128) −18
(129) −2a¿¿
(130) 3b2
(131) 2
(132) 3
(133) 27
(134) 0
(135) −43
(136) 2
(137) −1
(138) 89
(139) √153
(140) −122
(141) 12
(142) 32
(143) √305
(144) 0
(145) 2
(146) 12
(147) 5
(148) ∞
(149) ∞
(150) ∞
(151) ∞