Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Write the Value of Lim X → 1 − X − [ X ] . - Mathematics

Answer in Brief

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

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Solution

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

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