in a skew symmetric, how do we explain that its diagonal entries has to be all 0 without giving examples to support it

Answer 1

For the definition of a skew-symmetirc matrix, see
http://en.wikipedia.org/wiki/Skew-symmetric_matrix

The requirement for such a matrix is: aij = -aji

For the diagonal elememnts aii, clearly the requirement is that they be zero. A number can only equal its negative if it is zero.

Answer 2

lim x infinitive (4x-1/2x+9)