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quiz4_sols

quiz4_sols - 0[11 tf'i-1 r(1-1f-1 J I)C'I(I IY'1 J ~...

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QUIZ 4 Name: k f- Y REMEMBER!! Show details of your work and use correct notation. 1. (4+6 points) Let VXY f(x, y) = Ixl + Iyl a. Find the largest domain for f (x, y). y... 'j 7/ 0 - ,..~) ,+-"- ~~"'1"":., (~"'\.J;,) b e I 4\l .... It" ... ""'b. Ne ~ ...... , t"'\.le ........ Jt &L,..{Jo ""'",~ ~o-\--""'~ Lt.. +\L .,"':"\."- lO.~) b. Is it possible to define f(x, y) at (0, 0) in order to make f(x, y) continuous at (0, a)? If your answer is "Yes", define f(O,O) to obtain a continuous function at (0, 0). If your answer is "No", show that it is impossible to define f(O, 0) to obtain a continuous function at (0,0). L~'}- 'J:: ~ y, 'M '7 0 ~ ~'..., §t..: ~'~ V 1< ... y _ {)~ V~ ,t;:l:. 11' C"
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Unformatted text preview: 0) [11 tf'i} .,. -1\),)(, r '''')(1 -1f -1 J I)C'I (I + IY'1 J) ~ to", ,_1 .r;. . z: !M€ ;~(l"-ve ~ bI-) Ii rfv~1--~ .. ;}-~( ,. r: e".u. .. C 111 5'; ( ) ) e.A ~ e e..-pp t o4-(:f r~~;t 1'~o til l-t~) Ir1V\ . ... }'3 lo~o)I. .N{ d t r,'''fa-( I {_.-fA-Of 0.-C.."+I""~O"1) ..r~ "-f-(\J)O)] 2. (4 points) Given f(x, y) = x 2 + 3y 2 + 1. Sketch the graph of exactly one level cur e of f and give the equation of that level curve. \ .f l:. a.<. I '1-1. ,. !> f.1 '\t l.:" '<: :) )<,1. . t 3 'j 1. = l-( -, (k;>/ ,) 1.. ~-1-+~=1-..A:. ..--+--:r""""':? 1(,,1 If(.-I -r ~'t--- e 3. (6 points) Given f(x, y, z) = e YZ + xy In z, compute fyz...
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