Calculus III: Three Dimensional Coordinate Systems (Level 3 of 10)

The video tutorial explains how to graph equations in three-dimensional space using Cartesian coordinates. It covers graphing lines in the XY, YZ, and XZ planes, translating them into 3D, and understanding the implications of unexpressed variables. The tutorial also demonstrates graphing circles and parabolas, emphasizing the transition from 2D to 3D representations. The video aims to build foundational skills for navigating 3D coordinate systems, preparing viewers for more advanced multivariable calculus concepts.

What is the slope of the line represented by the equation y = x in R squared?

• 0

• 1

• 2

• -1

In the equation y = x, what does the absence of the variable z imply when graphing in R cubed?

• z is zero

• z can take any value

• z is negative

• z is positive

When graphing z = -2y + 1, what is the z-intercept on the yz plane?

• 2

• -1

• 1

• 0

What does the slope of -2 in the equation z = -2y + 1 indicate about the graph's direction?

• It is vertical

• It rises

• It is horizontal

• It falls

How do you convert the equation 2z + 1 = 3x into slope-intercept form?

• z = 3x + 1/2

• z = x/3 - 2

• z = 2/3x + 1

• z = 3/2x - 1/2

What is the z-intercept of the equation 2z + 1 = 3x when graphed on the xz plane?

• 3/2

• 1

• 0

• -1/2

What shape does the equation x^2 + y^2 = 4 represent in R cubed?

• Parabola

• Sphere

• Cylinder

• Plane

In the equation x^2 + y^2 = 4, what is the radius of the circle in R squared?

• 1

• 4

• 3

• 2

What type of surface does the equation z = x^2 represent in R cubed?

• Parabolic Cylinder

• Sphere

• Cylinder

• Plane

In the equation z = x^2, which variable is not expressed, allowing it to take any value?

• None

• z

• y

• x