278 EXAMPLES OP ELIMINATION". 



21. If z = * + < (- + logy] , then 



2 \X J 



dz ,dz 



ydy +x dx = y- 



22. Eliminate the functions from y = xf(z)+(f>(z). 



Result. The same as in Example 16. 



23. If z + mx + ny =f{ (x - a} 3 + (y - &)* + (z - c)*}, then 

 {y-l-n(z-c}}-^-{x-a-m(z-c)}-^ = n(x-a}-m(y-l}. 



24. If z = x 2 (ax + by) + <j> (y 3 + a*) + ^ (y* - x'}, 



1 d*z 1 <Fz l_dz 1_ dz _ 3a bx 



tlien a ~7 a ~~ ~3 7 2 "~" 3 ~~T~ "l" 3 ~T~ ~~ "l 3 * 



a; a 2 # 3 ay .or AB ^ ay a; y 



25. If s = <j> {x +/(y)}, then 



dxdy dx dy dx* 

 26. Eliminate the arbitrary functions from 



' 2i* 

 \x +y*J 



^*3 S<?*^ 



& -y ^. 



27. If w + # + 2; = x s f {x (u y), sc(y z}}, then 

 du . .du, .du 



28. If u=<}>{F( y *-xz}, f&jt-?j.-t)t, then 

 dy y dz dt ~ 



