This document contains the solutions to a list of calculus exercises from the second semester of 2006 regarding curves of level sets of functions of two variables. It provides the domain and image set for 9 functions and graphs the level curves for 6 of the functions.

1. &DOFXOR 4 VHPHVWUH GH 7XUPD 6HJXQGD OLVWD GH H[HUFu
u rFLRV
8)6DU ^ uOFXOR 7XUPD 6HJXQGD OLVWD GH H[HUFu
D rFLRV
4 VHPHVWUH GH 3URI -RaR 9 6DPSDLR
D
XUYDV GH Qu
rYHO GH IXQzRHV GH GXDV YDULuYHLV
Fa D
3DUD FDGD XPD GDV IXQzaHV GDGDV GHWHUPLQH VHX GRPu H HVERFH DOJXPDV DR PHQRV TXDWUR

2. GH
FR rQLR
VXDV FXUYDV GH Qu
rYHO 'HWHUPLQH WDPEuP R FRQMXQWRLPDJHP GD IXQzaR 6XJHVWaR 2 YDORU UHDO
H FD D
N HVWu QR FRQMXQWR LPDJHP GD IXQzaR I VRPHQWH TXDQGR D FXUYD GH Qu GH I FRUUHVSRQGHQWH D
D FD rYHO
] N u QaR YD]LD

3. H D
I [