Question

Write the value of $\underset{x\to 1^{-}}{\lim }x-\left[x\right].$

Answer 1

$$\begin{gathered} \underset{x\to 1^{-}}{\lim }\left(x-\left[x\right]\right) \\ x=1-h \\ \therefore h\to 0 \\ \underset{h\to 0}{\lim }\left(\left(1-h\right)-\left[1-h\right]\right) \\ =1-0 \\ =1 \end{gathered}$$