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If F ( X ) = { X 2 − 16 X − 4 , If X ≠ 4 K , If X = 4 is Continuous at X = 4, Find K. - Mathematics

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प्रश्न

If \[f\left( x \right) = \begin{cases}\frac{x^2 - 16}{x - 4}, & \text{ if }  x \neq 4 \\ k , & \text{ if }  x = 4\end{cases}\]  is continuous at x = 4, find k.

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उत्तर

Given: \[f\left( x \right) = \begin{cases}\frac{x^2 - 16}{x - 4}, & \text{ if }  x \neq 4 \\ k , & \text{ if }  x = 4\end{cases}\]

If  \[f\left( x \right)\]  is continuous at  \[x = 4\] , then

\[\lim_{x \to 4} f\left( x \right) = f\left( 4 \right)\]
\[\Rightarrow \lim_{x \to 4} \left( \frac{x^2 - 16}{x - 4} \right) = k\]
\[\Rightarrow \lim_{x \to 4} \frac{\left( x + 4 \right)\left( x - 4 \right)}{\left( x - 4 \right)} = k\]
\[ \Rightarrow \lim_{x \to 4} \left( x + 4 \right) = k\]
\[ \Rightarrow k = 8\]
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अध्याय 9: Continuity - Exercise 9.3 [पृष्ठ ४२]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 9 Continuity
Exercise 9.3 | Q 6 | पृष्ठ ४२

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