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Evaluate the Following One Sided Limit: Lim X → 2 − X − 3 X 2 − 4 - Mathematics

Evaluate the following one sided limit: 

\[\lim_{x \to 2^-} \frac{x - 3}{x^2 - 4}\] 

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Solution

\[\lim_{x \to 2^-} \left( \frac{x - 3}{x^2 - 4} \right)\]
\[\text{ Let } x = 2 - h, \text{ where } h \to 0 . \]
\[ \Rightarrow \lim_{h \to 0} \left[ \frac{2 - h - 3}{\left( 2 - h \right)^2 - 2^2} \right]\]
\[ = \lim_{h \to 0} \left[ \frac{- h - 1}{\left( 2 - h - 2 \right) \left( 2 - h + 2 \right)} \right]\]
\[ = \lim_{h \to 0} \left[ \frac{- h - 1}{\left( - h \right) \left( 4 - h \right)} \right]\]
\[ = \lim_{h \to 0} \left[ \frac{1 + h}{h\left( 4 - h \right)} \right]\]
\[ = \infty\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 13.02 | Page 11
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