LIMITES EXERCICIOS AUXILIARES

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LIMITES
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1. Calcule os limites:
a) 
		b) 
c) 
		d) 
e) 
_____________________________________
2. Determine:
a) 
		b) 
c) 
	d) 
e) 
	f) 
_____________________________________
3. Calcule:
a) 
		b) 
c) 
		d) 
_____________________________________
4. Ache o valor de:
a) 
		b) 
c) 
	d) 
_____________________________________
5. Calcule os limites:
a) 
b) 
_____________________________________
6. Calcule 
, em cada caso:
a) 
	
b) 
		c) 
d) 
		e) 
_____________________________________
7. Dada a função 
, calcule:
a) 
			b) 
c) 
			d) 
e) 
_____________________________________
8. Dada a função 
 diga se f(x) é contínua nos pontos:
a) x = 0	b) x = – 1	c) x = 2
_____________________________________
9. Seja m 
 R e f: R → R a função definida por: 
Calcular o valor de m para que f(x) seja contínua em x = 3.
_____________________________________
10. Dada a função 
, diga se f(x) é contínua nos pontos:
a) x = 5		b) x = 2
_____________________________________
11. Seja 
R e seja f: R → R a função definida por 
Calcule
 para que f(x) seja contínua em x=3.
12. Determine se a função f , definida por:
é contínua ou descontínua nos pontos:
a) x = 1		b) x = 3
_____________________________________
13. Mostre se a função 
é contínua ou descontínua em x = 3.
_____________________________________
14. Considere a função, definida em R por:
Calcular o valor de k para que a função seja contínua em x = 1.
_____________________________________
15. Dada a função:
Determinar m para que f(x) seja contínua em x = 2.
Sugestão: multiplicar o numerador e denominador pelo “conjugado” 
.
_____________________________________
16. A função contínua y = f(x) está definida no intervalo [– 4, 8] por:
Sendo a e b números reais.
Calcule os valores de a e b e esboce o gráfico cartesiano da função dada.
_____________________________________
17. Determine:
a) 
b) 
18. Determine: 
a) 
b) 
_____________________________________
19. Ache o valor de:
a) 
		b) 
_____________________________________
20. Calcule:
a) 
	
			
b) 
		
c) 
_____________________________________
21. Calcule:
a) 
			e) 
b) 
			f) 
c) 
			g) 
d) 
			h) 
_____________________________________
22. Calcule 
_____________________________________
23. Determine:
a) 
			c) 
b) 
		d) 
24. Calcule 
_____________________________________
25. Determine:
a) 
		c) 
b) 
		d) 
_____________________________________
26. Calcule:
a) 
	c) 
b) 
	d) 
_____________________________________
27. Calcule:
a) 
b) 
c) 
_____________________________________
28. Calcular 
_____________________________________
29. Ache o valor de 
_____________________________________
30. Calcular 
_____________________________________
31. Determine:
a) 
		b) 
_____________________________________
32. Determine 
33. Calcule 
_____________________________________
34. Calcule 
_____________________________________
35. Calcule:
a) 
		c) 
b) 
		d) 
_____________________________________
36. Calcule:
a) 
b) 
c) 
d) 
e) 
f) 
_____________________________________
37. Fatore as expressões e simplifique as frações para obter o valor de:
a) 
		c) 
b) 
			d) 
_____________________________________
38. Calcular o valor de 
_____________________________________
39. Determine:
a) 
	
b) 
c) 
		d) 
e) 
_____________________________________
40. Calcule 
_____________________________________
41. Multiplique o numerador e o denominador pelo “conjugado” de um deles para determinar:
a) 
		b) 
_____________________________________
42. Calcular o valor de 
_____________________________________
43. Calcular o valor da expressão 
_____________________________________
44. Determine o valor de 
Sugestão: multiplicar o denominador e numerador pelos “conjugados” de ambos.
_____________________________________
45. Calcular 
_____________________________________
46. Calcule 
_____________________________________
47. Calcule:
a) 
			b) 
_____________________________________
48. Determine: 
_____________________________________
49. Calcular o valor de 
_____________________________________
50. Dada a função 
 , calcule:
a) 
		b) 
51. Calcule:
a) 
		c) 
b) 
		d) 
_____________________________________
52. Calcule 
_____________________________________
53. Ache o valor de 
_____________________________________
54. Calcule:
a) 
		c) 
b) 
		d) 
_____________________________________
55. Calcular 
 para:
a) k = 0		b) k ≠ 0
_____________________________________
56. Calcular:
a) 
b) 
c) 
_____________________________________
57. Determine 
_____________________________________
58. Sejam 
R e a 
 R, a ≠ 0. Determine:
a) 
b) 
59. A função f: R → R, com
é contínua para x = 4. Calcular o valor de m.
_____________________________________
60. A função 
 não está definida para x = 1. Seja f(1) = k. Calcular o valor de k para que a função f(x) seja contínua no ponto x = 1.
_____________________________________
61. Esboce o gráfico da função e determine o limite:
a) 
		d) 
b) 
		e) 
c) 
		f) 
_____________________________________
62. Calcule:
a) 
		b) 
_____________________________________
63. Calcular os limites:
a) 
		b) 
_____________________________________
64. Calcule:
a) 
		b) 
_____________________________________
65. Esboce o gráfico da função e determine o limite:
a) 
		b) 
_____________________________________
66. Calcular:
a) 
		b) 
67. Esboce o gráfico da função e dê o valor de:
a) 
		b) 
_____________________________________
68. Calcule 
_____________________________________
69. Calcule:
a) 
		c) 
b) 
		d) 
_____________________________________
70. Determinar 
_____________________________________
71. Calcular o valor de 
_____________________________________
72. Ache o valor de 
_____________________________________
73. Determine 
_____________________________________
74. Determine:
a) 
b) 
_____________________________________
75. Calcule o valor de 
_____________________________________
76. Calcule:
a) 
		b) 
_____________________________________
77. Sabendo que 
, calcule 
78. Aplicando o limite exponencial fundamental, calcule:
a) 
	c) 
b) 
	d) 
_____________________________________
79. Ache o valor de 
_____________________________________
80. Calcule 
_____________________________________
81. Calcule 
_____________________________________
82. Determine 
_____________________________________
83. Calcule 
_____________________________________
84. Se 
, calcule ln a.
_____________________________________
85. Calcule 
.
Sugestão: 
_____________________________________
RECORDANDO
1. Calcule:
a) 
b) 
c) 
2. Ache o valor de 
.
_____________________________________
3. Seja λ um número real e seja f: R → R a função tal que:
Calcule λ para que exista 
_____________________________________
4. Sabendo-se que 
, x ≠ m, então podemos afirmar que:
m é maior do que 4
m é menor do que – 4
m 
 [1, 4]
m 
 [– 4, 1]
não existe m, tal que 
_____________________________________
5. Seja f definida por 
 
o valor de 
 é:
a) 1	b) 2	c) 3	d) 4	e) 5
_____________________________________6. Determine:
a) 
b) 
c) 
d) 
_____________________________________
7. Calcule 
_____________________________________
8. Determine m para que
 
9. Determine:
a) 
	b) 
_____________________________________
10. O valor de 
 é:
a) zero	 b) + ∞ c) – ∞ d) 2 e) 1
_____________________________________
11. Determine:
a) 
	
b) 
c) 
		d) 
_____________________________________
12.Calcule:
a) 
		b) 
c) 
		d) 
_____________________________________
13. Dada a função f: R → R, definida por 
, calcule 
_____________________________________
14. Calcule 
_____________________________________
15. Determine 
_____________________________________
16. Calcule:
a) 
	b) 
_____________________________________
17. Determine:
a) 
	b) 
18. Dada a função f: R → R tal que 
Determinar o valor de m de modo que f(x) seja contínua em x = 1.
_____________________________________
19. Calcule 
_____________________________________
20. Sabe-se que 
. Conclui-se que 
:
a) é 
		b) é 0		c) é infinito
d) é indeterminado		e) não existe
_____________________________________
21. Calcule 
_____________________________________
22. Calcule:
a) 
	b) 
_____________________________________
23. Determinar 
Sugestão: 
_____________________________________
24. Calcular 
Sugestão: 
_____________________________________
25. Determine 
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