Greatest integer and fractional part for JEE

Formula

\[x=[x]+\{x\},\qquad [x]\le x<[x]+1,\qquad 0\le \{x\}<1\]

Variables: \([x]\) is greatest integer function, \(\{x\}\) is fractional part.

Conditions: For real \(x\).

Discontinuity and graph questions, limits involving piecewise jumps.