Is Continuous At X = 0, Then Write The Value Of K.

English0CBSECommerce (English Medium) Class 12Question PapersQuestion Papers2587Textbook Solutions20345MCQ Online Mock Tests42Important Solutions22925Concept Notes & Videos606Time Tables24SyllabusIf F ( X ) = { X Sin 3 X , X ≠ 0 K , X = 0 is Continuous at X = 0, Then Write the Value of K. - Mathematics

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Question

If \[f\left( x \right) = \begin{cases}\frac{x}{\sin 3x}, & x \neq 0 \\ k , & x = 0\end{cases}\] is continuous at x = 0, then write the value of k.

Sum

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SolutionShow Solution

If \[f\left( x \right)\] is continuous at

\[x = 0\] , then \[\lim_{x \to 0} f\left( x \right) = f\left( 0 \right)\]

\[\Rightarrow \lim_{x \to 0} \frac{x}{\sin 3x} = k\]\[ \Rightarrow \lim_{x \to 0} \frac{1}{\frac{\sin 3x}{x}} = k\]\[ \Rightarrow \lim_{x \to 0} \frac{1}{\frac{3 \sin 3x}{3x}} = k\]\[ \Rightarrow \frac{1}{3}\left( \frac{1}{\lim_{x \to 0} \frac{\sin 3x}{3x}} \right) = k\]\[ \Rightarrow k = \frac{1}{3}\]

shaalaa.comAlgebra of Continuous Functions Report Error Is there an error in this question or solution?Q 4Q 3Q 5Chapter 9: Continuity - Exercise 9.3 [Page 41]

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RD Sharma Mathematics [English] Class 12Chapter 9 ContinuityExercise 9.3 | Q 4 | Page 41

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