test3_sol_Winter_08

# test3_sol_Winter_08 - to find ~z and ~z at the point ux uy...

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MATH 2008/09B Test 3 March 4,2008 NAME(PLEASE PRlNT): S.~/~ . ..c STUDENT NO.: . Instructions: 1. This test has 4 questions and a total of 40 marks. 2. Calculators are NOT allowed. . sin (2y'x2 + y2) (Ql) Let f(x, y) = JXL+YI if (x, y) #- (0,0) and f(O, 0) = 1; x +y (a) [5 Marks] Find lim. f(x, y), if exists, or show that the limit does not exist; (x,y)--(O,Oi =: -4~ £:=i;2 I ) (" '0~O-+ c /t, (d) [2 Marks] Find the largest set at whieh f is continuous.

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(Q2) (a) [6 Marks] Find the linearization of the function f(·I, y) = (VX + JY)2 at t.he point (xo, Yo) = (1,9); ( . '1 n ~._- .- - ) (/Of;;) -.~) ~ ~_~= #'_1
(Q3) Let S be the surface with equation ex2y2z2 -- x In(yz + 1) = x - 2y + z2 -1 and let the point P(l, 0, 1) lie on S; (a) [9 Marks] Use Implicit Function Theorem

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Unformatted text preview: to find ~z and ~z at the point ux uy P; 0-0-I ;::.-1';2. . 0-0-;;:&lt;' (j) U&gt;'/2f . {UI ~~\ ~h~'9f.~dJ~Ct(})' ( () _I +2-o-0-2-, 4' ';2 d 2:-f!jft ;/{ Ihy y-r-cl ff7 ~ cY';} 7liP(}Y'~ /.{p-nq{l/~ 5/9 pieafe ,I ~&quot;-\..,/ / (b) [3 Marks] Use part (a) to find a scalar equation of the tangent plane to the surface S at the point P. :::. (-Y2 ) Yz }-I ) (Q4) [8 Marks] Use The Chain Rule to find ~~ when r = 0 and 8 = 1 jf w = sin(xy) + eYz-In(xz), x = 1 + sin(r82), y = er62 and z = 1 + In(r82 + I),-[ CrY '1-1) \lCc;O ~-t-\ ~0 \ .-j-e. J l'\ eO~ + le-\~L~~...
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## test3_sol_Winter_08 - to find ~z and ~z at the point ux uy...

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