Important Questions [8]
- If U = E X Y Z F ( X Y Z ) Prove that X ∂ U ∂ X + Z ∂ U ∂ X 2 X Y Z U and Y ∂ U ∂ X + Z ∂ U ∂ Z = 2 X Y Z U and Hence Show that X ∂ 2 U ∂ Z ∂ X = Y ∂ 2 U ∂ Z ∂ Y
- Find the N^Th Derivative of X 3 ( X + 1 ) ( X − 2 )
- Find the Nth Derivative of Cos 5x.Cos 3x.Cos X.
- Evaluate Lim X → 0 Sin X Log X .
- Find Nth Derivative of 1 X 2 + a 2 .
- If Y = E Tan − 1 X .Prove that ( 1 + X 2 ) Y N + 2 + [ 2 ( N + 1 ) X − 1 ] Y N + 1 + N ( N + 1 ) Y N = 0
- If Y=Sin[Log(X2+2x+1)] Then Prove that (X+1)2yn+2 +(2n +1)(X+ 1)Yn+1 + (N2+4)Yn=0.
- If Y=(X+√X2-1 ,Prove that ( X 2 − 1 ) Y N + 2 + ( 2 N + 1 ) X Y N + 1 + ( N 2 − M 2 ) Y N = 0
