Questions asked by Shehroz B.

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• If f=x^3+y^3+z^3+3xy, then show that # x(partial f)/(partial x) + y (partial f)/(partial y) + z (partial f)/(partial z) = 3f#?
  
• If #f= x^2 y^2+2xy^2#, then show that #(partial ^2f)/(partial x partial y) = (partial ^2f)/(partial y partial x)#. obtain the value of #f_(xy)(1,1)# ?
  
• Verify Rolle theorem for function: f(x)= #x^3-6x^2+11x-6# in the interval [1,3] ?
  
• If #u= y/x+ z/x + x/y#, show that #x(partial u)/(partial x)+y(partial u)/(partial y)+z(partial u)/(partial z)=0# ?
  
• If #u= (1-2xy+y^2)^-1/2# , then show that #x(partial u)/(partial x)-y(partial u)/(partial y)= y^2u^3# ?
  
• Using elementary row and coloumn transformation compute rank of following matrices: #((25,31,17,43),(75,94,53,132),(75,94,54,134),(25,32,20,48))# ?