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Find: Lim X → 2 [ X ] - Mathematics

Find: \[\ \lim_{x \to 2} \left[ x \right]\] 

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Solution

\[\lim_{x \to 2} \left[ x \right]\]
\[\text{ LHL }: \]
\[ \lim_{x \to 2^-} \left[ x \right]\]
\[Let x = 2 - \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ 2 - h \right]\]
\[ = 1\]
\[\text{ RHL }: \]
\[ \lim_{x \to 2^+} \left[ x \right]\]
\[\text{ Let } x = 2 + \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ 2 + h \right]\]
\[ = 2\]
\[ LHL \neq RHL\]
\[\text{ Thus }, \lim_{x \to 2} \left[ x \right] \text{ does not exist } .\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 15.1 | Page 12
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