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Unformatted text preview: Part C For each statement below, say whether it is TRUE or FALSE. (Please do not use the abbreviations T and F.) If it is true, explain why; if it is false, give an example demonstrating that it is deﬁnitely false. C.1) (After Oct. 26, 8 pts.) If F and G are conservative vector ﬁelds on a region R , then F + G is conservative on R too. C.2) (After Oct. 26, 8 pts.) If P and Q are diﬀerentiable functions on the region R deﬁned by 4 < x 2 + y 2 < 9, and Q x (2 , 1) 6 = P y (2 , 1), then the vector ﬁeld h P ( x,y ) ,Q ( x,y ) i is not the gradient ﬁeld of any diﬀerentiable function on R . C.3) (After Oct. 29, 8 pts.) If R 1 and R 2 are simply connected regions, then so is their union R 1 ∪ R 2 . Reminder: Please write “Sources consulted: none” at the top of your homework, or list your (animate and inanimate) sources. See the course information sheet for details. 1...
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This note was uploaded on 09/14/2011 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08
- Multivariable Calculus