The function f(x) is defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\left| x \right|}}{x}}\\ {0,} \end{array}\begin{array}{*{20}{c}} {,x \ne 0}\\ {x = 0} \end{array}} \right.\) then, at x = 0 it is

• A. Continuous
• B. Discontinuous at x = 0 and has discontinuity of first kind
• C. Discontinuous at x = 0 and has removable discontinuity
• D. Discontinuous at x = 0 and has discontinuity of second kind