Exercises 2.1 1. y 2. y y x t x t 3. y 4. y y x x t 5. y 6. y x x 7. y 8. y x x 17 Exercises 2.1 9. y 10. y x x 11. y 12. y x x 13. y 14. y x x 15. Writing the differential equation in the form dy/dx = y(1 − y)(1 + y) we see that critical points are located at y = −1‚ y = 0‚ and y = 1. The phase portrait is shown below. -1 y 5 4 3 2 1 1 2 x 0 1 y (a) (b)
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physical security threats are: Ÿ Weather‚ e.g. temperature‚ humidity‚ water‚ flood‚ wind‚ snow‚ lightening‚ etc. Ÿ Fire and Chemical‚ e.g. explosion‚ smoke‚ toxic material‚ industrial pollution‚ etc. Ÿ Earth movement‚ e.g. earthquake‚ volcano‚ slide‚ etc. Ÿ Object movement‚ e.g. building collapse‚ falling object‚ car‚ truck‚ plane‚ etc. Ÿ Energy‚ e.g. electricity‚ magnetism‚ radio wave anomalies‚ etc. Ÿ Equipment ‚ e.g. mechanical or electronic component failure‚ etc. Ÿ Organism‚ e.g. virus‚ bacteria
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$10 each‚ and y of another product at a cost of $15 each‚ then the total cost to the firm is a function of two independent variables‚ x and y. By generalizing notation‚ the total cost can be written. C (x‚ y ) = 10x + 15y Dr. Nguyen Minh Quan (HCMIU-VNU) Chapter 2. Multivariable calculus Summer 2013 3 / 80 Introduction Example (Production cost) A company is developing a new soft drink. The cost in dollars to produce a batch of the drink is approximated by C (x‚ y ) = 2200 +
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Nike.inc SWOT analysis Strengths: y y y y y y y y y y y y y Nike is a globally recognized for being the number one sportswear brand in the World. Nike being a competitive organization has a healthy aver sion towards its competitors i.e. during Atlanta Olympics‚ Reebok expensed on sponsoring the games; Nike however sponsored the top athletes and due to this step‚ it gained valuable coverage. Nike has no factories; rather it uses contract factories to get the
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x + y = 4 (ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y Sol. (i) The given equation is x + y = 4 y = 4 – x …………….equation (1) Now ‚ putting the value x = 0 in equation (1) y = 4 – 0 = 4. So the solution is (0‚ 4) Putting the value x = 1 in equation (1) y = 4 – 1 = 3. So the solution is (1‚ 3) Putting the value x = 2 in equation (1) y = 4 – 2 = 2. So the solution is (2‚ 2) So‚ the table of the different solutions of the equation is (ii) The given equation is x - y = 2 x = 2 + y ……………
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one variable Let y = axb‚ where a and b are numbers‚ with b different from zero. The derivative of y with respect to x is dy/dx = abxb-1 Examples: y = 2x7‚ dy/dx = 2*7x7-1 = 14x6 y = 5x0.3‚ dy/dx = 5*0.3*x0.3-1 = 1.5x-0.7 Exercises: Calculate dy/dx a) y= 3x2 b) y = 12x0.8 c) y = 6 e) y = 5/x4 g) y = 3 f) y = 4x2 + 2/x3 d) y = +4/ h) y = 8x Another useful derivative rule is for the natural logarithm. Let y = ln x‚ for x>0. Then‚ dy/dx = 1/x Example: y = 5 lnx‚ dy/dx =
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of X and eight units of Y give a consumer the same utility as four units of X and two units of Y. Over this range: a. If the consumer obtains one more unit of X‚ how many units of Y must be given up in order to keep utility constant ∆Y∆X=2-84-2= - 62= -3 ~ Utility unchanged‚ if consumer exchanges 3 units of Y for 1 unit of X. b. If the consumer obtains one more unit of Y‚ how many units of X must be given up in order to keep utility constant? ∆Y∆X= 4-22-8= 26= -13
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1. Describa y evalúe el producto‚ los negocios y las estrategias corporativas de Giordano. • Producto Ventas al detalle de ropa casual para hombre mujer y niños en cuatro marcas: Giordano‚ Giordano Ladies‚ Giordano Junior y Giordano Blue Star Exchange (BSE) Giordano Tiendas situadas en distritos de compras al detalle con mucho tránsito de personas a pie. Ropa casual en un inicio para hombre y después unisex‚ a precios razonables‚ imagen de marca moderna. Giordano ladies Elegantes blusas
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la guerra y la paz‚ oscilando entre el énfasis a políticas represivas para hacer frente al conflicto armado con la insurgencia y la promoción de procesos de paz encaminados a encontrar una solución negociada. No obstante las políticas de seguridad y paz de los distintos gobiernos‚ sólo se han logrado acuerdos parciales de paz con algunos grupos guerrilleros‚ pero en cambio el conflicto se ha escalado a niveles de intensidad significativos. En ese contexto se ha generado una importante y masiva movilización
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1 region must be created with every line. 2. Two consecutive lines cannot be drawn parallel 3. If a line crosses through an intersection already formed by other lines‚ it does not count as an extra point of intersection 4. n: number of lines y: Number of bounded or unbounded regions x: number of intersects When x number of lines are drawn‚ how many unbounded regions are formed? *RULES: 1. The first 2 lines drawn must be perpendicular 2. The line drawn must go from one side all the
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