UNIDAD 1: TAREA 1
LEDHERZON CONTRERAS PINTO Cod 1.122.647.465 JOSE NORBEY TORRES 1122650665 CRISTIAN LEONARDO CELY Cod 1.122.652.834 EDILBERTO LOPEZ
Cod
13520245
OMAR ANDRES NIÑO JIMENEZ
DIEGO FRANCISCO MARTINEZ
CALCULO DIFERENCIAL
GRUPO 100410_694
CUMARAL (META) 27 DE AGOSTO DE 2018
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Introducción
Este trabajo se adquirió conocimientos sobre los temas de funciones y sucesiones del curso de cálculo diferencial, temas que eh realizado se dio para resolver temas de Geogebra ubicar su vértice la pendiente y temas relacionado con que se trabajó en esta plataforma. Ahora como es un trabajo colaborativo se trabajara consolidando el trabajo de los demás compañeros del grupo.
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Estudiante 1: LEDHERZON CONTRERAS PINTO 1. La grafica muestra el número de Autos vendidos por un concesionario en los últimos 3 años. De acuerdo con esta grafica conteste a. ¿Cuáles son la variable dependiente e independiente? independiente? Respuesta: La variable independiente son los meses del año y la variable dependiente es la cantidad de autos vendidos. b. ¿En qué momento del año 2016 se venden menos menos autos? Respuesta: Se venden menos autos en el mes de Agosto c. ¿En qué año se vendieron más autos? Justifique su respuesta. Respuesta: Se venden en el año 2016 ya que la variable pendiente dice que se vendieron un aproximado de 975 autos d. ¿En qué año se vendieron menos autos? autos? Justifique su respuesta. Respuesta: Se vendieron menos autos en el año 2016 en el mes de agosto ya que la variable pendiente dice que se vendieron un promedio de 75 autos.
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2. Determine el rango y dominio de la siguiente función:
()=+2 X
F(x)
-2
6
-1
3
0
2
1
3
2
6
()=+2 = 2 2 = 4+2 = 6
Dominio (f) = son todos los números Reales Rango (f) = [2, ∞)
3. Construya de su autoría las siguientes siguientes funciones de acuerdo con su tipo tipo y los parámetros especificados en la tabla:
Función Lineal Función Polinómica Función Radical Función Racional Función Trigonométrica
Variable dependiente x z c t a
Variable Independiente y t d u b
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y: variable independiente x= my + b x = 2y+ 4
Función Polinómica: z: variable dependiente t: variable independiente
2 3t6 2 3t6
z (t)= z=
Función Radical: c: Variable dependiente d: Variable Independiente c(d)= 4 - √d+2
Función Racional t: variable dependiente u: variable independiente
= 42 Función Trigonométrica a: variable dependiente
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4. Hallar la ecuación de la recta que pasa por por los puntos:
3,2 3, 2 1,2 Especificar también la pendiente
de la recta.
= x 4 = 1 = 22 = 13 4 Ahora con la pendiente se procede a calcular la ecuación de la recta haciendo uso de la ecuación: y
−
= m( x x − )
y - 2 = 1(x - 3) y – 2 = x – 3 y – 2 – x + 3 = 0
–x + y + 1= 0 –1 (-x+y+1) x – y –1 y = x – 1
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5. Dada la siguiente sucesión determine:
a. Si converge o diverge
= 2 3
La sucesión es divergente porque van aumentando y tiene un límite límite infinito (∞). a. Sus 5 primeros términos.
13 4
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= 5 2 3 = 82 = 4 b. Sus cotas superior e inferior (si las tiene) tiene) -
Cota superior:
→∞ 3 →∞ 2 3 1 ∞3 1 0 1 2 = ∞2 = 0 = 0 = ∞ No tiene Cota superior ya que su resultado resu ltado es -
Cota inferior:
Cota inferior 2
∞
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GRAFICAS – GEOGEBRA
Realizar las gráficas en Geogebra de acuerdo con los lineamientos brindados en el OVI “Funciones en Geogebra”.
Realizar una interpretación para cada una de las gráficas obtenidas, estableciendo claramente tipo de función, rango y dominio, puntos de intersección, vértice (si lo tiene) y asíntotas (si las tiene). Este análisis debe realizarse en un párrafo para cada gráfica asignada relacionando la captura de pantalla de cada una de las gráficas obtenidas en Geogebra
Entregar gráficas e interpretación escrita en documento .doc, durante la semana (2) en el foro de desarrollo de la actividad (entorno de aprendizaje colaborativo), dejando clara evidencia de participación significativa.
Estudiante 1.
a.
= 2+2
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Esta función es de tipo lineal con pendiente m=1 por lo tanto es creciente y por lo tanto cuyos puntos de intersección son: el eje y (0,2) y en el eje x (-1,0) su dominio corresponde a todos los valores en x pertenecientes a los números reales: dominio (-∞, ∞); { } y su rango a todos los valores en y perteneciente a los números reales rango (-∞, ∞); { } esta función no tiene vértice ni asíntotas.
x| x|x ∈ ℝ
b.
=
x| x|x ∈ ℝ
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Esta función es tipo potencia ya que el valor de A>0 la parábola abre hacia arriba cuyos puntos de intersección son: el eje y (0,0) y el eje x (0,0), su dominio corresponde a todos los valores en desde el menos infinito hasta el más infinito: Dominio (- ∞, ∞); { } y su rango a todos los valores en a los los números números pertenecientes a los números reales . Su vértice es el desde 0 hasta más Infinito (∞): rango punto más bajo el cual coincide con la intersección en (0,0). Esta función no tiene asíntotas.
c.
= 34
x|x ∈ ℝ
[0;∞;{y|y≥0}
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Esta función es de tipo racional y tiene punto de intersección en el eje
= 3.0 .
=
y
punto de intersección en el eje El dominio de la función corresponde a El todos los valores en correspondientes a los números reales. Su rango de la función: La Función tiene una asíntota vertical de y asíntota horizontal de . Esta función no tiene vértice.
€ℝ{1} =1
=2
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Estudiante 2: José Norbey Torres.
1.La gráfica muestra el número de autos vendidos por un concesionario en los últimos 3 años. De acuerdo con esta gráfica conteste: a.
¿Cuales son la variable dependiente e independiente?
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En junio ya que nos muestra su punto mas alto. =750 unidades c.
¿En qué año se vendieron más autos? Justifique su respuesta.
Mes Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Septiemb re Octubre Noviembre Noviembr e Diciembre Diciembr e
2016 150 350 240 130 550 350 250 450 350 250 450 350
2017 250 400 550 650 350 750 250 350 250 350 550 570
2018 450 650 850 350 350 350 530 650 650 620 770 780
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f(x)=x^4-2 12000 10000 8000 6000 4000 2000 0 -15
- 10
-5
0
5
-2000
x
f(x) -10
9998
10
15
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El dominio de la función es (-∞,∞) tal que todo x pertenece a los números R
El rango de la función es el intervalo [- 2,∞) tal que todo y sea mayor o igual que -2 3.
Construya de su autoría las siguientes funciones de acuerdo con su tipo y los parámetros especificados especificados en la tabla: Variable dependiente Función lineal Función polinómica Función radical Función racional
Variable independiente
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a. Si converge o diverge b. Sus 5 primeros términos
1 21
Trigonometría A= senb Hallar la ecuación de la recta que pasa por los puntos:
=
4,1 4, 1 1, 1, 3
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c. Sus 5 primeros términos
34 , 14 , 14 , 34 , 54 c.
Sus cotas superior e inferior (si las tiene)
no tiene cotas.
Estudiante 3 CRISTIAN LEONARDO CELY 1)
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= 3 58 Función radical: = √ 5 − Función Racional: = + Función Trigonométrica: = cos Función polinómica:
4.
4,1 1, 1,3 3
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1 161 17 4 4= 2 = 2 = 2 1 251 24 5 5 = 2 = 2 = 2 = 12 a) Como 1 > entonces es una secesión divergente. b) Ver procedimiento anterior c) No tiene tiene cota superior por ser una sucesión divergente Una cota inferior es el cero (0)
Graficas a)
y=5x1
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Tiene una asíntota vertical en Tiene una asíntota vertical en
= 2 = 1
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Estudiante 4 EDILBERTO PÉREZ 1. La gráfica muestra el número de autos vendidos por un concesionario en los últimos 3 años. De acuerdo con esta conteste: a. ¿Cuáles son las variables dependiente e independiente? independiente?
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