supplement to BOB p6 - Supplement to BOB (page 6) 9.8, #13b...

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Supplement to BOB (page 6) 9.8, #13b div v div Ð0 Ñœ Ò0@ß0@ß0@Óœ p "#$ `Ð0@ Ñ `B `C `D (product rule) œ 0 @ 0 0 `@ `0 "# $ div v • v œ0 ß ß Ò@ß@ß@Óœ0 f0 pp Š‹ $ 9.9, #6 ÒD ß B ß C Ó sin sec cos # 9.9, #16d curl(grad ) curl i j k œ ppp ’“ ââ ``` œ ß ß œ ! p ’Š `C`D `D`C `B`D `D`B `B`C `C`B ## #### (as long as all partials are continuous) 10.1, #4 r p Ð>Ñ œ Ò# >ß # ! Ÿ > Ÿ cos sin 1 ' G F • r p p "' $ 10.1, #8 ' ! # > # "Î) "" #% " # $ cosh sinh sinh cosh Ð> Ñß / "ß #>ß $> .> œ  /  Ð"  "Ñ ¸ !Þ')&( 10.3, #10 '' !B B BC $ BC/ .C .B œ / "# ' 10.4, #9 Since F is the gradient of a scalar function, the line integral is path independent, and p therefore its value around the closed curve is zero. G 10.5, #13 BOB's answer is correct. Here is another correct answer. r N p Ð?ß@ÑœÒ?ß@ß Ð"'%?#@ÑÓ
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