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Unformatted text preview: F is conservative. If it is, ﬁnd a scalar potential function for F . (a) ( § 6.3 no.4) F = 2 x sin y i + x 2 cos y j . (b) F = yz 2 i + ( x + xz 2 ) j + 2 xyz k . 4. ( § 6.3 no.22) Let f,g , and h be functions of class C 1 of a single variable. (a) Show that F = ( f ( x ) + y + z ) i + ( x + g ( y ) + z ) j + ( x + y + h ( z )) k is conservative. (b) Determine a scalar potential for F . (Your answer will involve integrals of f,g , and h .) (c) Find R C F · d s , where C is any path from ( x ,y ,z ) to ( x 1 ,y 1 ,z 1 ). 1...
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This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.
- Spring '11
- Multivariable Calculus