7/24/2019 Clculo 3-Chau (PUCP)

1/228

Rectas y Planos en R^3

Calculo 3 pgina 1

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2/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

3/228

puntos.

Calculo 3 pgina 3

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4/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

5/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

6/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

7/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

8/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

9/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

10/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

11/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

12/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

13/228

Posiciones Relativas entre Rectas y Planos

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

14/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

15/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

16/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

17/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

18/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

19/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

20/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

21/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

22/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

23/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

24/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

25/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

26/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

27/228 Calculo 3 pgina 15

7/24/2019 Clculo 3-Chau (PUCP)

28/228

Sistemas Lineales (cont.)

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

29/228

Algebra Matricial

Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

30/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

31/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

32/228

7/24/2019 Clculo 3-Chau (PUCP)

33/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

34/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

35/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

36/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

37/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

38/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

39/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

40/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

41/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

42/228 Calculo 3 pgina 15

7/24/2019 Clculo 3-Chau (PUCP)

43/228 Calculo 3 pgina 16

7/24/2019 Clculo 3-Chau (PUCP)

44/228 Calculo 3 pgina 17

7/24/2019 Clculo 3-Chau (PUCP)

45/228 Calculo 3 pgina 18

7/24/2019 Clculo 3-Chau (PUCP)

46/228

7/24/2019 Clculo 3-Chau (PUCP)

47/228

7/24/2019 Clculo 3-Chau (PUCP)

48/228

Determinantes

Calculo 3 pgina 1

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49/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

50/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

51/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

52/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

53/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

54/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

55/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

56/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

57/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

58/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

59/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

60/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

61/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

62/228

Transformaciones Lineales de R^n en R^m

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

63/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

64/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

65/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

66/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

67/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

68/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

69/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

70/228

Semana 6

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

71/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

72/228

Si un conjunto finito de funciones es linealmente dependiente, entonces su matriz de Wronski siempre tiene

determinante cero (esta afirmacin es el contrarrecproco de la afirmacin de arriba).

Si W(x_0) es singular (esto es, tiene determinante cero) para algn x_0, no se puede afirmar que el conjunto A es

linealmente dependiente.

Algunas observaciones:

Si la matriz de Wronski de un conjunto finito de funciones reales tiene determinante cero en un intervalo, entonces

existe un subintervalo donde el conjunto es linealmente dependiente.

Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

73/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

74/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

75/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

76/228

Ejercicios Resueltos

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

77/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

78/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

79/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

80/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

81/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

82/228

Transformaciones Lineales

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

83/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

84/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

85/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

86/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

87/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

88/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

89/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

90/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

91/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

92/228

Ejercicios Resueltos

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

93/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

94/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

95/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

96/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

97/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

98/228

La esfera

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

99/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

100/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

101/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

102/228

7/24/2019 Clculo 3-Chau (PUCP)

103/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

104/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

105/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

106/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

107/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

108/228

7/24/2019 Clculo 3-Chau (PUCP)

109/228

7/24/2019 Clculo 3-Chau (PUCP)

110/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

111/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

112/228

Funciones Vectoriales de Variable Real

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

113/228

7/24/2019 Clculo 3-Chau (PUCP)

114/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

115/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

116/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

117/228

7/24/2019 Clculo 3-Chau (PUCP)

118/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

119/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

120/228

7/24/2019 Clculo 3-Chau (PUCP)

121/228

7/24/2019 Clculo 3-Chau (PUCP)

122/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

123/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

124/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

125/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

126/228 Calculo 3 pgina 15

7/24/2019 Clculo 3-Chau (PUCP)

127/228 Calculo 3 pgina 16

7/24/2019 Clculo 3-Chau (PUCP)

128/228

Derivada e Integral de una Funcion Vectorial. Longitud de Arco

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

129/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

130/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

131/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

132/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

133/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

134/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

135/228

Parametrizacin Longitud de Arco

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

136/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

137/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

138/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

139/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

140/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

141/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

142/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

143/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

144/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

145/228

7/24/2019 Clculo 3-Chau (PUCP)

146/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

147/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

148/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

149/228

Repaso Examen Parcial de Cal-3viernes, 11 de octubre de 2013

Calculo Numrico pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

150/228 Calculo Numrico pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

151/228 Calculo Numrico pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

152/228 Calculo Numrico pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

153/228

Completar.

Calculo Numrico pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

154/228

Funciones Reales de Varias Variables

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

155/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

156/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

157/228

Funciones de Dos Variables

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

158/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

159/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

160/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

161/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

162/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

163/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

164/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

165/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

166/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

167/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

168/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

169/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

170/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

171/228

Derivadas Parciales

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

172/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

173/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

174/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

175/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

176/228

Derivadas Parciales (cont.)

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

177/228

7/24/2019 Clculo 3-Chau (PUCP)

178/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

179/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

180/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

181/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

182/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

183/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

184/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

185/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

186/228

7/24/2019 Clculo 3-Chau (PUCP)

187/228

P4-Problemas Resueltos

viernes, 15 de noviembre de 2013

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

188/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

189/228

Gradiente y Derivada Direccional

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

190/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

191/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

192/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

193/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

194/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

195/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

196/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

197/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

198/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

199/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

200/228

Valores Extremos

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

201/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

202/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

203/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

204/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

205/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

206/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

207/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

208/228

Metodo de Multiplicadores de Lagrange

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

209/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

210/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

211/228 Calculo 3 pgina 4

7/24/2019 Clculo 3-Chau (PUCP)

212/228 Calculo 3 pgina 5

7/24/2019 Clculo 3-Chau (PUCP)

213/228 Calculo 3 pgina 6

7/24/2019 Clculo 3-Chau (PUCP)

214/228 Calculo 3 pgina 7

7/24/2019 Clculo 3-Chau (PUCP)

215/228 Calculo 3 pgina 8

7/24/2019 Clculo 3-Chau (PUCP)

216/228 Calculo 3 pgina 9

7/24/2019 Clculo 3-Chau (PUCP)

217/228 Calculo 3 pgina 10

7/24/2019 Clculo 3-Chau (PUCP)

218/228 Calculo 3 pgina 11

7/24/2019 Clculo 3-Chau (PUCP)

219/228 Calculo 3 pgina 12

7/24/2019 Clculo 3-Chau (PUCP)

220/228 Calculo 3 pgina 13

7/24/2019 Clculo 3-Chau (PUCP)

221/228 Calculo 3 pgina 14

7/24/2019 Clculo 3-Chau (PUCP)

222/228 Calculo 3 pgina 15

7/24/2019 Clculo 3-Chau (PUCP)

223/228 Calculo 3 pgina 16

7/24/2019 Clculo 3-Chau (PUCP)

224/228 Calculo 3 pgina 17

7/24/2019 Clculo 3-Chau (PUCP)

225/228

Ejercicios Resueltos de Exmenes Pasadosviernes, 29 de noviembre de 2013

Calculo 3 pgina 1

7/24/2019 Clculo 3-Chau (PUCP)

226/228 Calculo 3 pgina 2

7/24/2019 Clculo 3-Chau (PUCP)

227/228 Calculo 3 pgina 3

7/24/2019 Clculo 3-Chau (PUCP)

228/228