   Chapter 12.6, Problem 1E

Chapter
Section
Textbook Problem

# (a) What does the equation y = x2 represent as a curve in ℝ2?(b) What does it represent as a surface in ℝ3?(c) What does the equation z = y2 represent?

(a)

To determine

To describe: The representation of equation y=x2 in 2.

Explanation

2 is the two-dimensional coordinate system that contains x- and y-coordinates.

The equation y=x2 in 2 represents {(x,y)|y=x2}, which is the set of all points that intersect and form a parabola

(b)

To determine

To describe: The representation of equation y=x2 in 3.

(c)

To determine

To describe: The representation of equation z=y2 in 3.

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