Question

1. (18 pts.) Short answer: a) Given that f (u,v,w,x, y,z) is a real valued function, what dimension is its graph in? What dimension are its level curves in? (2,1,3). b) Given: g(x,y,z)= x? In (xy+z) Find the direction of maximum ascent c) Find I using integration or geometry: I = 6 dx dy. S: 146 d) Describe and/or draw the region: R= P ={(2,0,0)|9=%;05057; p=17}

Answer 1

flu, v, w, x, y, 2) is real valued function 7 dimension is its graph in has function is in 6 variables. Because that graph of f(x) Know AS in 2 dimension f (x, y) in 3 dimension same for b he direction of maximum ascent at (2,1,3) gradient of glx, 4, 2) = x² enlay+2) 12, 1,3) Ig (2, 1,3 gradient (ge2, 4, 2] (2,1,30 V81,3,2)=([**Lastzos Jenny + 2)24], a? :) 1 2 xy + 2 (xy + 2) 2 23 2 x2y 22 lentay+2) + (xy+2) 42 x 4+2 22 1 + 2*2 ( en 12.1+3)), 23 2² 1 2.1+3 Vg (2, 1,3 = 2.1+3 2.1 +3 ulus ما اه 19 (2,1,3) = lum

C) I - 6 dxdy 2 3 -2 S. 6[3-1-2] > 30 [y] - 308(21-2) I = 60 the Region R = £18,0,0) | = 416 ososa S=17 relation Blw spherical coondi nates Know the Rectangular and Z NU X 09 KR ie its half cone in the direction af positive yr Axis.