For each of the following vector fields F , decide whether it is conservative or

Question

For each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, ?f=F). If it is not conservative, type N.

A. F(x,y)=(?16x+8y)i+(8x+2y)j
f(x,y)=

B. F(x,y)=?8yi?7xj
f(x,y)=

C. F(x,y,z)=?8xi?7yj+k
f(x,y,z)=

D. F(x,y)=(?8siny)i+(16y?8xcosy)j
f(x,y)=

E. F(x,y,z)=?8x2i+8y2j+1z2k
f(x,y,z)=

Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

Explanation / Answer

a)-8x^2+8xy+y^2 b)not conservative c)-4x^2-7/2y^2+z d)-8xsiny+8y^2 e)-8/3x^3+8/3y^3+1/2z^2

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.