Exercise · ZW-LEVEL-CURVE-005 · ★★☆ Intermediate
For \(f(x,y)=x^2+y^2\), for which values of \(c\) is the level curve \(f(x,y)=c\) empty?
Choose one option.
Show answer
- D. For \(c<0\)
Explanation
Since \(x^2+y^2\ge 0\), no point has a negative value. For \(c=0\) the curve is just the origin, not empty.
Review the concept: Level curve
A level curve of a function \(f\) of two variables is the set of points in the plane where \(f\) takes one same constant value \(c\).
\[f(x,y)=c\]
More practice problems: level curve
- ZW-LEVEL-CURVE-001 For f(x,y)=x^2+y^2, what is the level curve f(x,y)=4?
- ZW-LEVEL-CURVE-002 The level curve f(x,y)=3 of f(x,y)=2x-y is the line:
- ZW-LEVEL-CURVE-003 Which point lies on the level curve f(x,y)=1 of f(x,y)=x^2-y?
- ZW-LEVEL-CURVE-004 What is the level curve f(x,y)=0 of f(x,y)=xy?
- ZW-LEVEL-CURVE-006 Can two different level curves of the same function f intersect?
- ZW-LEVEL-CURVE-007 The level curve f(x,y)=4 of f(x,y)=x^2+4y^2 meets the x-axis at:
- ZW-LEVEL-CURVE-008 For f(x,y)=x^2+y^2, how many times larger is the radius of the level curve f=9 than that of f=1?
- ZW-LEVEL-CURVE-009 For f(x,y)=(y)/(x), the level curve f(x,y)=2 is: