xy Let f(x,y) = x, if (x, y) + 0 (0, if (x, y)=(0,0) a. Show that fis continuous at (0, 0). b. Show that(x, 0) = x V x, and c. Show that (0,0) # (0,0). If = th (0,y) = - =y\y. , find the value of n for which the relation (2) (200) = 3 i If u log(x + y + z3 - 3xyz), show that 9 a. + + u = - (x+y+z)2* b. azu au au + + dx2 ay2 az au +2+2- +2 au 9 (x+y+z)2 Verify Euler's theorem for the function: a. (x + y) +y) (x + y) b. sin-1x n1 + tan c. log (x+2). 12.If u = csc-1(x+y is true. . Prove that x azu \x3+y ax2 +2xy au +y202 tan u Jy2 144 (13+ tan u) 13 a. If u = zx ,v= , W= ,then show that (u,v,w) a(x,y,z)) = 4 b. If xp cos,y=psino,z=z, show that (u,v,w) =P a(p.,z)) 14. a.lf z = f(x, y), where x =u2v2 and y = 2uv, prove that a2z a2z Ju Jv2 + =4(u + v). az ax ay2 Jz + b. If u =(x-y,y-z,z-x), show that + + = 0 ax ay dz c. If z f(x,y), where xe" -e" and y = e-"-e", show that az z z Ju = x -y dv