Concept explainers
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. If F = 〈–y, x〉 and C is the circle of radius 4 centered at (1.0) oriented counterclockwise, then
b. If F = 〈x, –y) and C is the circle of radius 4 centered at (1, 0) oriented counterclockwise, then
c. A constant vector field is conservative on ¡2.
d. The vector field F = 〈f(x), g(y)〉 is conservative on ¡2 (assume f and g are defined for all real numbers).
e. Gradient fields are conservative.
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Calculus: Early Transcendentals (2nd Edition)
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