Given the function f ( x‚ y ) = x 2 + 2 y 2 − 1 a. Find the domain and range of the function. (2 marks) b. Sketch the contour map of the function f ( x‚ y ) using three level curves‚ c = 1‚ 2‚ 3 . (4 marks) c. Use 3D-contour map to sketch roughly the surface of f ( x‚ y ) . (2 marks) 2 4 x2 − y 2 ‚ x2 + 2 y 2 f ( x‚ y ) along x- axis and y-axis‚ Given the function f ( x‚ y ) = a. find the lim ( x ‚ y )→(0‚0) (4 marks) b. does the lim ( x ‚ y )→(0‚0) f ( x‚ y ) exist? (1 marks)
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(Female: F;AR;PR;ST;M;CY;RI;D;Y) x (Male: AR;ST;RI;D;Y) Offspring Phenotype Number Proportion Ratio Female: AR;RI;Y 1 0.0010 1.000 Female: AR;ST;RI;Y 4 0.0039 4.000 Male: F;AR;M;RI;Y 1 0.0010 1.000 Male: F;AR;ST;M;RI;Y 4 0.0039
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1. (a) 4 x 3 y 24 Ans: a (b) 3x 4 y 25 (c) x y 7 (d) 3x 4 y 7 0 Sol: By formula required equation is given by x y 2 4 x 3 y 24 3 4 2. The equation of the line which is the perpendicular bisector of the line joining the points 3‚ 5 and 9‚3 is (a) 4 x 3 y 14 0 Ans: d Sol: A 3‚ 5 B 9‚3 Midpoint of AB 6‚ 1 . Slope of AB Slope of perpendicular line (b) 3x 4 y 14 0 (c) 3x 4 y 14 0 (d) 3x 4 y 14 0 8 4
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( x) > g ( y) . In order to solve it‚ you must put it in the form of dx g( y ) > dy = f ( x ) > dx allowing you to integrate. Your goal is to get an equation in the form of y = h( x) A differential equation will be in the form of dy = y2 dx ! y #2dy = dy 2 x = dx y 1) ! y dy = ! 2 x dx y = ± 2x2 + C 4) ! ! dx 2) y #1 = x+C #1 #1 y= x+C y2 = x2 + C 2 dy = 4y dx dy ! y= dy x + sin( x ) = 3y 2 dx dy = ky dx dy ! y= ! 4 dx
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Organization y Decentralized‚ Divisional Organization y 4 Product divisions y y y y 4 Manufacturing divisions 6 Staff offices Each division and staff office is headed by a V.P. Staff personnel have no line authority in a division 75% of the manufacturing sales is made to the product divisions‚ Parts made by the manufacturing division is designed by the product division. Transfer Prices y The divisions are expected to deal with one another as though they were independent companies. y Parts transferred
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write the standard form equation of each circle. 1) 8 x + x 2 − 2 y = 64 − y 2 2) 137 + 6 y = − y 2 − x 2 − 24 x 3) x 2 + y 2 + 14 x − 12 y + 4 = 0 4) y 2 + 2 x + x 2 = 24 y − 120 5) x 2 + 2 x + y 2 = 55 + 10 y 6) 8 x + 32 y + y 2 = −263 − x 2 7) Center: (−11‚ −8) Radius: 4 8) Center: (−6‚ −15) Radius: 5 9) ( x − 16) 2 + ( y − 6) 2 = 1 Translated 4 left‚ 2 up 10) ( x + 5) 2 + ( y + 7) 2 = 36 Translated 5 left‚ 4 down 11) 12) y y 7 1 6 −1 1 2 3 4 5 6 x 5 −1 4 −2 3 −3 2 −4 1 −5 −4
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x-axis. Its coordinates are (#‚0). -The y-intercept of a line is the point where a line crosses the y-axis. Its coordinates are (0‚#). 1- Find the x-intercept by letting y=0. 2- Find the y-intercept by letting x=0. 3- Plot the intercepts and graph the line. (If the x and y intercepts are both 0‚ use a table to find the second point.) Ex: x-int: 5x-3y=-30 y=0 5x-3(0)=-30 5x=-30 –– –– 5 5 x= -6 (-6‚0) y-int: x=0 5(0)-3y=-30 –– –– -3 -3 y=10 (0‚10) The Slope-Intercept Method:
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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the following areas‚ Recruitment‚ Travel‚ Motors‚ Business‚ Property‚ Entertainment‚ Loans and Finance‚ Sports. and Retail. Companies that have previously advertised with The Daily Record are : Ÿ Ramsay World travel Ÿ DFS Furniture Ÿ First Glasgow Ÿ Arnold Clark Automobiles Ÿ DF Concerts Ÿ Distribution and Readership The Daily Record is Scotland’s best-red daily newspapers. The paper has a total circulation of 328‚001 and a readership of 952‚000. The newspaper is available throughout
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Learning Management Systems (LMS) Market [Products (Content Management‚ Student Management‚ Performance Management‚ Collaboration‚ Administration)‚ by Users (K-12‚ Higher Education‚ Corporate)] - Worldwide Market Forecasts and Analysis 2013 2018 On 26th June 2014 Learning Management Systems (LMS) refer to software applications used for planning‚ delivering‚ managing‚ and appraising a learning process. LMS uses web-based technology to create and deliver content‚ track and evaluate performance
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