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2. Consider the function z = f(x, y) = 2x+y-2. a) What shape is the graph of z=f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2.

2. Consider the function z = f(x, y) = 2x+y-2. a) What shape is the graph of z=f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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B 2. Consider the function z = f(x, y) =2x+y - 2. a) What shape is the graph of z= f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2. d) Sketch a graph of the level curves in part c by hand in the space below. 5 54 3 2 1 0 1 2 3 4 2 3 -3 -5 56* e) Sketch a graph of z = f(x, y) in the space below. You are welcome to use graphing software for this, such as CalcPlot3D. as 901 rtial Derivat Bahaan plots on the r Prac #5, page Prac #5, page 3
Transcribed Image Text:B 2. Consider the function z = f(x, y) =2x+y - 2. a) What shape is the graph of z= f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2. d) Sketch a graph of the level curves in part c by hand in the space below. 5 54 3 2 1 0 1 2 3 4 2 3 -3 -5 56* e) Sketch a graph of z = f(x, y) in the space below. You are welcome to use graphing software for this, such as CalcPlot3D. as 901 rtial Derivat Bahaan plots on the r Prac #5, page Prac #5, page 3
B 2. Consider the function z = f(x, y) =2x+y - 2. a) What shape is the graph of z= f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2. d) Sketch a graph of the level curves in part c by hand in the space below. 5 54 3 2 1 0 1 2 3 4 2 3 -3 -5 56* e) Sketch a graph of z = f(x, y) in the space below. You are welcome to use graphing software for this, such as CalcPlot3D. as 901 rtial Derivat Bahaan plots on the r Prac #5, page Prac #5, page 3
Transcribed Image Text:B 2. Consider the function z = f(x, y) =2x+y - 2. a) What shape is the graph of z= f(x,y)? Does the graph pass through the origin? b) Find the points where the graph of z = f(x, y) intersects each of the x, y, and z-axes. c) Find the equations of the level curves for z = 0, z = 1, and z = 2. d) Sketch a graph of the level curves in part c by hand in the space below. 5 54 3 2 1 0 1 2 3 4 2 3 -3 -5 56* e) Sketch a graph of z = f(x, y) in the space below. You are welcome to use graphing software for this, such as CalcPlot3D. as 901 rtial Derivat Bahaan plots on the r Prac #5, page Prac #5, page 3
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