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) ∞