Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 1]_Basic Notions_183
1790*. Let * = V7+/(l/x 1). Determine the functions / and
z if z = x when y= 1.
1791**. Letz = */(-V Determine the functions f and z if
when x=\.
1792. Find and sketch the domains of definition of the following
functions:
a) z==Y\ x 2
b) z=\-\-V (x
c) z =
y 2
d) 2 - x + arc cos //;
e) z-l/l-^ 2
+
f) z = ' arc sin ;
X
g) 2 r = V 7IT
h) 2 =
\
1793. Find the domains of the following functions of three
arguments:
a) u=-\x + y + z\ c) w=--arc sin jc+arc sin # + arc sinz;
b) u = ln(xyz): d) u = V\x2
1794. Construct the level lines of the given functions and determine
the character of the surfaces depicted by these functions:
a) z^x + y; d) z =
b) 2 = ^+y 2
; e) z =
c) z = x*-y*; O^
1795. Find the level lines of the following functions:
a) z = ln(*'+f/); d) z = /(y a*);
b) 2 = ar
1796. Find the level surfaces of the functions of three independent
variables:
a) u = x + y-\-z;
* ' '
b) u =
c) u = J
y 2
z\