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lim x → 2 x 4 − 16 x − 2 - Mathematics

\[\lim_{x \to 2} \frac{x^4 - 16}{x - 2}\] 

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Solution

\[\lim_{x \to 2} \left[ \frac{x^4 - 16}{x - 2} \right]\]
\[\text{ It is of the form } \frac{0}{0} . \]
\[ \lim_{x \to 2} \left[ \frac{\left( x^2 \right)^2 - \left( 4 \right)^2}{x - 2} \right]\]
\[ = \lim_{x \to 2} \left[ \frac{\left( x^2 - 4 \right)\left( x^2 + 4 \right)}{x - 2} \right]\]
\[ = \lim_{x \to 2} \left[ \frac{\left( x - 2 \right)\left( x + 2 \right)\left( x^2 + 4 \right)}{x - 2} \right]\]
\[ = \left( 2 + 2 \right)\left( 2^2 + 4 \right)\]
\[ = 32\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.3 | Q 7 | Page 23
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