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For What Value of K is the Function F ( X ) = { Sin 2 X X , X ≠ 0 K , X = 0 Continuous at X = 0? - Mathematics

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प्रश्न

For what value of k is the function

\[f\left( x \right) = \begin{cases}\frac{\sin 2x}{x}, & x \neq 0 \\ k , & x = 0\end{cases}\]  continuous at x = 0?

 

योग

उत्तर

Given: 

\[f\left( x \right) = \binom{\frac{\sin2x}{x}, x \neq 0}{k, x = 0}\]

If f(x) is continuous at x = 0, then

\[\lim_{x \to 0} f\left( x \right) = f\left( 0 \right)\]
\[\Rightarrow \lim_{x \to 0} \frac{\sin2x}{x} = k\]
\[\Rightarrow \lim_{x \to 0} \frac{2\sin2x}{2x} = k\]
\[\Rightarrow 2 \lim_{x \to 0} \frac{\sin2x}{2x} = k\]
\[\Rightarrow 2 \times 1 = k\]
\[\Rightarrow k = 2\]
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अध्याय 9: Continuity - Exercise 9.1 [पृष्ठ १९]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 9 Continuity
Exercise 9.1 | Q 29 | पृष्ठ १९

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