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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
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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
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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
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