![(b) (6 marks] Given that f(z) = 2x2 + y - 4y2 +i(4xy – 2x2 + 32). (1) Is f differentiable? 1](http://img.homeworklib.com/questions/bfab0d00-16cd-11ec-a1af-0bd22e1896a2.png?x-oss-process=image/resize,w_560)
Homework Answers
EXAMPLE 1 Find the tangent plane to the elliptic paraboloid z = 2x2 + 4y2 at...
EXAMPLE 1 Find the tangent plane to the elliptic paraboloid z = 2x2 + 4y2 at the point (1, 1, 6). SOLUTION Let f(x, y) = 2x2 + 4y. Then f(x, y) = fy(x, y) = fx(1, 1) = fy(1, 1) = Then this equation gives the equation of the tangent plane at (1, 1,6) as (x + 1) + (y - 1) Z or ZE
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multipl...
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7 For 18-2...
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coo...
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
f(x,y) = 2x2 + 4y2 + 3xy - 44x 95y +580 barrels of fertilizer are produced...
f(x,y) = 2x2 + 4y2 + 3xy - 44x 95y +580 barrels of fertilizer are produced when x kilograms of ingredie and y liters of ingredient Y are combined. Check: F(2, 3) = 269 Use this context and the graph provided below to answer the next FOUR questions. y liters (3.5, 4.5) f barrels * kilograms (3.5,4,5) f barrels x kilograms 1. Find af дх at (3.5, 4.5). Select II. What are the units on Of , Select] ax III....
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z =...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
f(x, y) = 2x2 + 4y2 + 3xy 44x 95y +580 barrels of fertilizer are produced...
f(x, y) = 2x2 + 4y2 + 3xy 44x 95y +580 barrels of fertilizer are produced when x kilograms and y liters of ingredient Y are combined. Check: f(2,3) = 269 Use this context and the graph provided below to answer the next FOUR questions. y liters (3.5, 4.5) Sbarrels x kilograms af I. Find at (3.5, 4.5 (Select ] ax -48.5 -2.939 - 16.5 -0.340 II. What are the units on ? barrels per kilogram II. What are the...
A flow has a velocity field defined by V={(?2x2?2y2)i+(?4xy)j}, where x and y are in feet....
A flow has a velocity field defined by V={(?2x2?2y2)i+(?4xy)j}, where x and y are in feet. Determine the equation for the equipotential line passing through point (3 ft, 2 ft). Express your answer in the form y2=f(x). If the potential function does not exist, answer "rotational." Express your answer in terms of x.
The joint density of X and Y is given as f(x, y) = 4xy, 0 <...
The joint density of X and Y is given as f(x, y) = 4xy, 0 < x, 1 and 0 < y < 1. (a). Find the marginal distribution of Y, fY (y). (b). Find E[X|Y = 1/2]. (c). Find P(X < .3|Y < .2).
The joint density of X and Y is given as f(x, y) = 4xy, 0 <...
The joint density of X and Y is given as f(x, y) = 4xy, 0 < x, 1 and 0 < y < 1. (a). [6pts] Find the marginal distribution of Y, fY (y). (b). [6pts] Find E[X|Y = 2]. (c). [6pts] Find P(X < .3|Y < .2)
EXAMPLE 1 Find the tangent plane to the elliptic paraboloid z = 2x2 + 4y2 at the point (1, 1, 6). SOLUTION Let f(x, y) = 2x2 + 4y. Then f(x, y) = fy(x, y) = fx(1, 1) = fy(1, 1) = Then this equation gives the equation of the tangent plane at (1, 1,6) as (x + 1) + (y - 1) Z or ZE
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks] (c) Use Lagrange Multiplier to find the absolute maximum and minimum of 10 (x,y)-x +y subject to 2 12 marks
6. (a) Find the directional derivative of f(, y,z)at Po(1,10 in the direction of u-i-2j+k. 4 marks] (b) Letz201), where f is a differentiable function, show that 08z 4 marks]...
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
f(x,y) = 2x2 + 4y2 + 3xy - 44x 95y +580 barrels of fertilizer are produced when x kilograms of ingredie and y liters of ingredient Y are combined. Check: F(2, 3) = 269 Use this context and the graph provided below to answer the next FOUR questions. y liters (3.5, 4.5) f barrels * kilograms (3.5,4,5) f barrels x kilograms 1. Find af дх at (3.5, 4.5). Select II. What are the units on Of , Select] ax III....
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
f(x, y) = 2x2 + 4y2 + 3xy 44x 95y +580 barrels of fertilizer are produced when x kilograms and y liters of ingredient Y are combined. Check: f(2,3) = 269 Use this context and the graph provided below to answer the next FOUR questions. y liters (3.5, 4.5) Sbarrels x kilograms af I. Find at (3.5, 4.5 (Select ] ax -48.5 -2.939 - 16.5 -0.340 II. What are the units on ? barrels per kilogram II. What are the...
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