Let `A(0,1),B(1,1) ,C(1,-1) ,D(-1,0)` be four points. If P is any other point, then `PA+PB+PCPDged`, when `[d]` is where `[.]` represents greatest integer.

The curve passing through the point (1,1) satisfies the differential equation (dy)/(dx)+(sqrt((x^2-1)(y^2-1)))/(x y)=0 . If the curve passes through the point (sqrt(2),k), then the value of [k] is (where [.] represents greatest integer function)_____

Find x satisfying [tan^(-1)x]+[cot^(-1)x]=2, where [.] represents the greatest integer function.

Prove that [lim_(xto0) (tan^(-1)x)/(x)]=0, where [.] represents the greatest integer function.

Prove that [lim_(xrarr0) (sinx.tanx)/(x^(2))]=1 ,where [.] represents greatest integer function.

Let A=[{:(,0,1),(,1,1):}],B=[{:(,1,1),(,0,1):}] be any two bollean matrices of the same type find A vv B and A wedge B