Question

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

Answer 1

\[\lim_{x \to 1^-} \left( x - \left[ x \right] \right)\]
\[ x = 1 - h\]
\[ \therefore h \to 0\]
\[ \lim_{h \to 0} \left( \left( 1 - h \right) - \left[ 1 - h \right] \right)\]
\[ = 1 - 0\]
\[ = 1\]