Cal_C_test_3_b

# Cal_C_test_3_b - \J V'r 4"P-ra cfw Test3 MA 201-02.l Name...

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Test 3 MA 201-02 \ \J V--- ' -ra 'r 4"P {\ \ \-\\.l Name show all work for full creditl No books' notes' calculators' conversationewithfriendsnetc.area|lowed! 1. a) (20 pts) Find the Jacobian of the change of variables t = ttrw ' y = tlvrr '; i ).r ,.rY \ - i . i'-,' 't'i , 1u'" t-ni.' t--r i .,' ,, ,,ri - t*'i , \ : '-J i", ''r ; ', if ;vr",\$'" - w,J') * tJ (ti*'f * )l l:v'J +;)vr-** J 1--r';;-13 bi (10 pts) Find the rec-tangular coordinates of the point whose spherical --la -{.n z.) ,a: . ,-.,i * !' coordinates are |.o, , "tJ .,. ..r. .t ',: I :' r' ii-'- '\'''-''- '".1. ., ' -\ *-. 1' , i1i i r\r/ : * \,j v 1 a: I 'h /i \ I I \'\^--r 1 I I \ I \ y' -!; Y: f\$in*#* \' rtf:Se u);ir#S"f X'' 61;ru: - ttr',, i .ar, F. 6_ ! nd, _? , ..rr-,j \Jr: r. . g [ft*] { - 3fs 2. (30 pts) Use cylindrical coordinates to evalu""J{l y'dV, where E is the solid that fies within the cylinder x2 + !? =7' above the plane z = 0 ' and below the cone z2 = 4x2 + 4v2 " s\\- v. clv i*' -- 4 x'_' dy *,--o .lij: I *' *,, i

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## This note was uploaded on 06/04/2010 for the course MA 1256 taught by Professor Marples during the Spring '10 term at UAA.

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Cal_C_test_3_b - \J V'r 4"P-ra cfw Test3 MA 201-02.l Name...

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