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X-2do-Repaso (Sin solucionario).pptx
1.
Curso: ÁLGEBRA Tema: REPASO Grado: Semana: SEGUNDO 40
2.
DESIGUALDA DES SEMANA 36
3.
EJERCICIO 1 :
𝑆𝑖: −1 ≤ 𝑥 < 3 𝐼𝑛𝑑𝑖𝑐𝑎𝑟 𝑙𝑎 𝑣𝑎𝑟𝑖𝑎𝑐𝑖ó𝑛 𝑑𝑒 𝐸 = 𝑥 + 3 RESOLUCIÓN :
4.
EJERCICIO 2 :
𝑆𝑖: −5 < 𝑥 ≤ 4 𝐼𝑛𝑑𝑖𝑐𝑎𝑟 𝑙𝑎 𝑣𝑎𝑟𝑖𝑎𝑐𝑖ó𝑛 𝑑𝑒: 𝑀 = 3𝑥 + 5 RESOLUCIÓN :
5.
EJERCICIO 3: 𝑆𝑖:
−20 ≤ 2𝑥 ≤ 8 𝐼𝑛𝑑𝑖𝑐𝑎𝑟 𝑙𝑎 𝑣𝑎𝑟𝑖𝑎𝑐𝑖ó𝑛 𝑑𝑒 ∶ 𝑀 = −3𝑥 RESOLUCIÓN :
6.
EJERCICIO 4 : ¿
𝐶𝑢á𝑛𝑡𝑜𝑠 𝑛ú𝑚𝑒𝑟𝑜𝑠 𝑒𝑛𝑡𝑒𝑟𝑜𝑠 ∶ 𝑃 𝑥 = 3 − 𝑥 ; 𝑒𝑥𝑖𝑠𝑡𝑒𝑛 𝑠𝑖 𝑠𝑒 𝑠𝑎𝑏𝑒 𝑞𝑢𝑒 ∶ 2 < 𝑥 ≤ 7 ? RESOLUCIÓN :
7.
EJERCICIO 5 :
𝑆𝑖: −2 < 𝑥 ≤ 2 𝐼𝑛𝑑𝑖𝑐𝑎𝑟 𝑙𝑎 𝑣𝑎𝑟𝑖𝑎𝑐𝑖ó𝑛 𝑑𝑒 𝐾 = 10 3 − 𝑋 RESOLUCIÓN :
8.
EJERCICIO 6 :
𝑆𝑖 ∶ 5 ≤ 𝑥 − 1 𝑥 + 2 ≤ 12 𝐼𝑛𝑑𝑖𝑐𝑎𝑟 𝑙𝑎 𝑣𝑎𝑟𝑖𝑎𝑐𝑖ó𝑛 𝑑𝑒 "𝑥" RESOLUCIÓN :
9.
SEMANA 37
10.
EJERCICIO 1 : RESOLUCIÓN
: 𝑆𝑖: 𝐴 = −5; 8 ∪ 10; +∞ 𝐵 = 1; 17 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒: 𝐴 ∩ 𝐵
11.
EJERCICIO 2 :
𝑅𝑒𝑙𝑎𝑐𝑖𝑜𝑛𝑎𝑟 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑎𝑚𝑒𝑛𝑡𝑒: RESOLUCIÓN : −𝟓 ≤ 𝒙 < 𝟕 A −𝟐; 𝟕 B 𝒙 ≤ 𝟕 C −𝟓; 𝟐 D −5 2 −5 7 −2 7 7
12.
EJERCICIO 3: RESOLUCIÓN : 𝑆𝑖
∶ 𝑥 ∈ −7; 2 , 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑟 𝑔𝑟á𝑓𝑖𝑐𝑎𝑚𝑒𝑛𝑡𝑒 𝑒𝑙 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙𝑜 𝑑𝑒 ∶ 𝐸 = 𝑥 + 4
13.
EJERCICIO 4 : RESOLUCIÓN
: 𝑆𝑖 ∶ 5 − 𝑥 ∈ 1; 7 , 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑟 𝑔𝑟á𝑓𝑖𝑐𝑎𝑚𝑒𝑛𝑡𝑒 𝑒𝑙 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙𝑜 𝑑𝑒 ∶ 𝑀 = 𝑥2 − 1
14.
EJERCICIO 5 : RESOLUCIÓN
: 𝑆𝑖 ∶ 𝐴 = −6; −3 ∪ 3; 7 𝐵 = −∞; −4 ∪ 3; +∞ 𝐻𝑎𝑙𝑙𝑎𝑟 ∶ 𝐴 ∪ 𝐵
15.
EJERCICIO 6 : RESOLUCIÓN
: 𝐸𝑛 𝑐𝑎𝑑𝑎 𝑐𝑎𝑠𝑜 ℎ𝑎𝑙𝑙𝑎 ∶ 𝐴 ∩ 𝐵 𝑎) −∞ +∞ +∞ +∞ +∞ −∞ −∞ +∞ −∞ −∞ −4 7 0 5 −2 7 𝑑) 𝐴 𝐵 𝐴 −7 0 4 6 𝑏) −3 𝐵 𝐴 𝑒) −1 1 𝐴 𝐵 𝑐) 0 5 7 𝐴 𝐵 𝐵
16.
SEMANA 38
17.
EJERCICIO 1: RESOLUCIÓN 𝑰𝒏𝒅𝒊𝒒𝒖𝒆 𝒆𝒍
𝒊𝒏𝒕𝒆𝒓𝒗𝒂𝒍𝒐 𝒔𝒐𝒍𝒖𝒄𝒊ó𝒏 𝒅𝒆: 𝒂) 𝟐𝒙 𝟑 − 𝟏 < 𝟏 𝟔 𝒃) 𝟐 − 𝒙 𝟑 ≥ 𝟏 𝟐
18.
EJERCICIO 2: RESOLUCIÓN 𝑰𝒏𝒅𝒊𝒄𝒂𝒓 𝒗𝒆𝒓𝒅𝒂𝒅𝒆𝒓𝒐
𝑽 𝒐 𝒇𝒂𝒍𝒔𝒐 𝒇 𝒆𝒏 𝒍𝒂𝒔 𝒔𝒊𝒈𝒖𝒊𝒆𝒏𝒕𝒆𝒔 𝒑𝒓𝒐𝒑𝒐𝒔𝒊𝒄𝒊𝒐𝒏𝒆𝒔 𝑰. 𝟕 ≤ 𝒙 + 𝟒 < 𝟏𝟏 ⇒ 𝒙 ∈ 𝟑; 𝟕 𝑰𝑰. 𝟐 < 𝒙 − 𝟐 < 𝟓 ⇒ 𝒙 ∈ 𝟒; 𝟕 𝑰𝑰𝑰. 𝟒 < 𝟑𝒙 + 𝟓 𝟐 ≤ 𝟕 ⇒ 𝒙 ∈ 𝟏; 𝟑
19.
EJERCICIO 3: RESOLUCIÓN 𝑹𝒆𝒔𝒐𝒍𝒗𝒆𝒓: 𝟑 𝒙
+ 𝟏 𝒙 − 𝟏 − 𝟐 𝒙 + 𝟐 𝒙 − 𝟐 ≥ 𝒙 − 𝟏 𝟐 ¿ 𝑪𝒖á𝒍 𝒅𝒆 𝒍𝒐𝒔 𝒔𝒊𝒈𝒖𝒊𝒆𝒏𝒕𝒆𝒔 𝒗𝒂𝒍𝒐𝒓𝒆𝒔 𝒏𝒐 𝒆𝒔 𝒔𝒐𝒍𝒖𝒄𝒊ó𝒏 𝒑𝒂𝒓𝒂 𝒍𝒂 𝒊𝒏𝒆𝒄𝒖𝒂𝒄𝒊ó𝒏? 𝒂) − 𝟔 𝒃) − 𝟏 𝒄) 𝟏 𝒅) 𝟑 𝒆) 𝟔
20.
EJERCICIO 4: RESOLUCIÓN 𝑹𝒆𝒔𝒐𝒍𝒗𝒆𝒓 𝒆𝒍
𝒔𝒊𝒈𝒖𝒊𝒆𝒏𝒕𝒆 𝒔𝒊𝒔𝒕𝒆𝒎𝒂: 𝒙 + 𝟒 𝒙 − 𝟓 ≤ 𝒙 − 𝟏 𝒙 + 𝟐 … (𝑰) 𝒙 − 𝟐 𝒙 + 𝟐 ≤ 𝒙 + 𝟑 𝒙 − 𝟒 … (𝑰𝑰)
21.
EJERCICIO 5: RESOLUCIÓN 𝑯𝒂𝒍𝒍𝒆 𝒆𝒍
𝒄𝒐𝒏𝒋𝒖𝒏𝒕𝒐 𝒔𝒐𝒍𝒖𝒄𝒊ó𝒏 𝒅𝒆𝒍 𝒔𝒊𝒔𝒕𝒆𝒎𝒂 𝒅𝒆 𝒊𝒏𝒆𝒄𝒖𝒂𝒄𝒊𝒐𝒏𝒆𝒔 𝑰. 𝟐𝒙 + 𝟏 𝟑 ≤ 𝒙 𝑰𝑰. 𝒙 − 𝟏 𝟐 < 𝒙 − 𝟑 𝑰𝑰𝑰. 𝒙 + 𝟑 𝟐 ≥ 𝒙 − 𝟔
22.
EJERCICIO 6: RESOLUCIÓN 𝑹𝒆𝒔𝒐𝒍𝒗𝒆𝒓 𝒆𝒍
𝒔𝒊𝒔𝒕𝒆𝒎𝒂: 𝐼) 𝑥 2 − 𝑥 + 1 3 < 1 𝐼𝐼) 𝑥 − 3 2 + 𝑥 3 > 1
23.
SEMANA 39
24.
EJERCICIO 1: RESOLUCIÓN Representar gráficamente
las siguientes expresiones: a) −𝟑 < 𝒙 ≤ 𝟎 b) 𝟓 ≤ 𝒙 < 𝟏𝟐 c) − 𝟏 𝟓 < 𝒙 < 𝟏 𝟗
25.
EJERCICIO 2: RESOLUCIÓN 𝐑𝐞𝐬𝐨𝐥𝐯𝐞𝐫 𝐞𝐥
𝐬𝐢𝐬𝐭𝐞𝐦𝐚 𝐞𝐧 𝐞𝐧𝐭𝐞𝐫𝐨𝐬 𝐩𝐨𝐬𝐢𝐭𝐢𝐯𝐨𝐬: 𝐱 + 𝐲 < 𝟓 𝐱 − 𝐲 > 𝟏 𝐈𝐧𝐝𝐢𝐜𝐚𝐫 𝐱𝐲 ……. (1) ……. (2)
26.
EJERCICIO 3: RESOLUCIÓN 𝐑𝐞𝐬𝐨𝐥𝐯𝐞𝐫 𝐞𝐧
𝐞𝐧𝐭𝐞𝐫𝐨𝐬 𝐩𝐨𝐬𝐢𝐭𝐢𝐯𝐨𝐬: 𝐱 𝟑 + 𝐲 𝟒 < 𝟐 … (𝟏) 𝐱 𝟑 − 𝐲 𝟒 > 𝟎 … (𝟐) 𝐲 > 𝟐 𝐈𝐧𝐝𝐢𝐜𝐚𝐫 𝐞𝐥 𝐯𝐚𝐥𝐨𝐫 𝐝𝐞 "𝐱𝟐 + 𝐲𝟐"
27.
EJERCICIO 4: RESOLUCIÓN 𝐑𝐞𝐬𝐨𝐥𝐯𝐞𝐫 𝐞𝐥
𝐬𝐢𝐬𝐭𝐞𝐦𝐚 𝐞𝐧 𝐞𝐧𝐭𝐞𝐫𝐨𝐬 ∶ 𝟐𝐱 − 𝟒𝐲 > 𝟐𝟎 𝐱 + 𝟓𝐲 < −𝟒 𝐲 > −𝟒 𝐈𝐧𝐝𝐢𝐜𝐚𝐫 𝐞𝐥 𝐦𝐞𝐧𝐨𝐫 𝐯𝐚𝐥𝐨𝐫 𝐝𝐞: (𝐱𝐲) ……. (1) ……. (2) ……. (3)
28.
EJERCICIO 5: RESOLUCIÓN Mathias 𝐭𝐢𝐞𝐧𝐞
𝐜𝐢𝐞𝐫𝐭𝐚 𝐜𝐚𝐧𝐭𝐢𝐝𝐚𝐝 𝐝𝐞 𝐝𝐢𝐧𝐞𝐫𝐨, 𝐠𝐚𝐬𝐭𝐚 𝟏𝟐𝟎 𝐬𝐨𝐥𝐞𝐬 𝐲 𝐥𝐨 𝐪𝐮𝐞 𝐥𝐞 𝐪𝐮𝐞𝐝𝐚 𝐞𝐬 𝐦á𝐬 𝐪𝐮𝐞 𝐥𝐨𝐬 𝟐 𝟑 𝐝𝐞 𝐥𝐨 𝐪𝐮𝐞 𝐭𝐞𝐧𝐢𝐚 𝐢𝐧𝐢𝐜𝐢𝐚𝐥𝐦𝐞𝐧𝐭𝐞; 𝐠𝐚𝐬𝐭𝐚 𝐥𝐮𝐞𝐠𝐨 𝐥𝐚 𝐦𝐢𝐭𝐚𝐝 𝐲 𝐞𝐥 saldo es 𝐦𝐞𝐧𝐨𝐫 𝐪𝐮𝐞 𝟏𝟑𝟎 𝐬𝐨𝐥𝐞𝐬. ¿ 𝐂𝐮á𝐧𝐭𝐨 𝐭𝐞𝐧í𝐚 𝐢𝐧𝐢𝐜𝐢𝐚𝐥𝐦𝐞𝐧𝐭𝐞, 𝐬𝐢 𝐞𝐬𝐞 𝐦𝐨𝐧𝐭𝐨 𝐞𝐬 𝐦ú𝐥𝐭𝐢𝐩𝐥𝐨 𝐝𝐞 𝟏𝟎?
29.
EJERCICIO 6: RESOLUCIÓN 𝐒𝐞 𝐜𝐨𝐦𝐩𝐫𝐚:
𝟐𝟎𝐱 𝐧𝐚𝐫𝐚𝐧𝐣𝐚𝐬, ; 𝐬𝐢 𝐬𝐞 𝐯𝐞𝐧𝐝𝐞 𝐥𝐚𝐬 𝐭𝐫𝐞𝐬 𝐜𝐮𝐚𝐫𝐭𝐚𝐬 𝐩𝐚𝐫𝐭𝐞𝐬, 𝐪𝐮𝐞𝐝𝐚𝐧 𝐦𝐞𝐧𝐨𝐬 𝐝𝐞 𝟏𝟏𝟎 𝐩𝐨𝐫 𝐯𝐞𝐧𝐝𝐞𝐫 𝐲 𝐬𝐢 𝐬𝐞 𝐯𝐞𝐧𝐝𝐢𝐞𝐫𝐚 𝐥𝐚 𝐪𝐮𝐢𝐧𝐭𝐚 𝐩𝐚𝐫𝐭𝐞 𝐪𝐮𝐞𝐝𝐚𝐫𝐢𝐚 𝐦𝐚𝐬 𝐝𝐞 𝟑𝟐𝟎 𝐩𝐨𝐫 𝐯𝐞𝐧𝐝𝐞𝐫. ¿ 𝐂𝐮á𝐧𝐭𝐚𝐬 𝐦𝐚𝐧𝐳𝐚𝐧𝐚𝐬 𝐬𝐞 𝐜𝐨𝐦𝐩𝐫𝐚𝐫𝐨𝐧?
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