quiz_04 - Use T.C o FO4/0L41/01 o Multivariable Calculus...

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Unformatted text preview: Use T.C. o. FO4/0L41/01 o Multivariable Calculus 16s MATH 2451 quiz_04 25 min Exam Course (Last Name) \u). m M“ t S r :L W; Ink gmesé Mg. m w A M st®®®ew 0 2016-02-03 (Wed) McCary . L. ,Lwflhp \.,._...J\..x . @QIGQT re x_ / ‘- \ J. \2/ , ‘ .1/ HUN. .s .. .. .. w pier/Gav? @@[email protected]@fi@ [email protected]@®@®@@®®®@w®®®®®@ @©®©®®®WO®®®@W®®M®®@ JDDxDfi \u .QD r/‘x @®@©@@k [email protected]@@@®®@ 1 a..\ V @@@®@®®@®®@®@®@®®@®©®@@[email protected] [email protected]@@@@@ [email protected]©®@®®®@ /?©@@@@®@®@@@@@@ @@©®©@m EQV @®@@®J A @ Q @ ® @ ® @ ® @ @ ® ® @ ® ,@@@@@@@@@®Qfl UM© Duration Due Date Instructor 0 Net ID 2016—02-03 01:12 Q. Fo4/0L4/o2 O 1. (10 points) (3.) Give an example of a'set A C R whichjs open. 5.57, 3/ 5531;" (b) Give an example of a set B C R which is closed. @- m + \/ (C) Give an example of a set C C R Wweither open nor closed. Eeéea Give an example of a set D C R which is both open and closed (such sets are called clopen, hint: there’s just L/ two of them for R). f x‘ n,- / (e) A set E C R2 is depicted. Plot the requested sets. \j)?7 Ira-3" 'Igg \- ‘ 135151; l I E ' gm. NPATQ‘C l. _ _';-€i 00 F04/0L4/0L Q j] points) Evaluate the following limit by converting to polar coordinates (5, 5 is not required). i—m 1111a (3 “55”? 1og(||£||'2)) for a e R2 FEM: J, Grader Only J, /\;H\-"" (“\flf‘» f‘“.’"“""\ (">1 f\ '89,: ‘1‘ o L 5 5/ {7 '8: I91 "5.; «.1 \:.i/' \g/ k.) \u \i/ \._..4 v K2. O. Fo4/0L4/04 . 3. (10 points) The function p(t) = on 0 S t < 211' parametrizes the unit circle. Let f : R2 -+ R2 be giVe _. 2 _. ' . . . . f(:c-) = [D 3:, and g : [0, 271-) —> R be glven as g(t) = “(f o p)(t)|]2. Fmd the mamma of 9 (both the value of th mafima and the I tiorgs) where they occur). 195?”): fiwllflz’ ’ ' . :9 - J, E r_ In 1/ \‘I ,7 f k“ f— fir" :Ti' 21/ a.) i jg” :5 gr 3 . \" k' 1/" x, " 1‘7 .xj J : 2C0§JQ +E~Z§wje r, L )5 3005,16 —— %H\J;€* ' 3co€j22§guf 77M: i: ,e ,e a W 3 M W: yew _. J, GraderOIflyL . O® . ...
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