1) Show that the follwing limit does not exist
lim(x,y)-(0,0)(xy+x2)/(x^2+y2)
2) Fin all the second orderpartial derivatives of
f(x,y,z)=x2tan-1(y+z)
3) Find the equation of thetangent plane to the surface
z=x2-4y2 atthe piont (1,2,-15).
4) Fin the linear approximation tothe function
f(x,y,z)=e-2xy+cos(2yz) at the point (1,-1,2)
5) Fin the normal vector to thesurface
z2=x2-y2 at the point (5,3,4)
6) You are standing on a surfacegiven by the equation
z=x2-2y2. Ifyou are standing at the poin (2,1,0), in which directio is thesteepest slope?
7) The temperature in the solarsystem is given by
T(x,y,z)=105/(x2+y2+z2). If acomet travels along the path r(t)=(t, t2-4, 2t), howfast is the temperatur changing when t=2?
8) Fin the critical point of thefunction f(x,y)= e4x-e-y. Use the secondderivative test to classifyf them, if possible.
9) Fin the extreme values off(x,y)=4x2+3y2 on the square 0 is less than or equal x,y less thanor equal to 1.
