Question

Write the value of ${lim}_{x\to 0^{-}}x-\left[x\right].$

Answer 1

${lim}_{x\to 0^{-}}x-\left[x\right]={lim}_{h\to 0}(1-h)-[1-h]={lim}_{h\to 0}(1-h)-0={lim}_{x\to 0^{-}}x-\left[x\right]=1$