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Discuss the Continuity of the Following Functions at the Indicated Point(S): (Ii) F ( X ) = { X 2 Sin ( 1 X ) , X ≠ 0 0 , X = 0 a T X = 0 - Mathematics

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प्रश्न

Discuss the continuity of the following functions at the indicated point(s): 

(ii) \[f\left( x \right) = \left\{ \begin{array}{l}x^2 \sin\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{array}at x = 0 \right.\]

उत्तर

Given:

\[f\left( x \right) = \binom{ x^2 \sin\frac{1}{x}, x \neq 0}{0, x = 0}\]

We observe

\[\lim_{x \to 0} x^2 \sin\left( \frac{1}{x} \right) = \lim_{x \to 0} x^2 \lim_{x \to 0} \sin\left( \frac{1}{x} \right) = 0 \times \lim_{x \to 0} \sin\left( \frac{1}{x} \right) = 0\]
\[\Rightarrow \lim_{x \to 0} f\left( x \right) = f\left( 0 \right)\]

Hence, f(x) is continuous at x = 0.

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पाठ 9: Continuity - Exercise 9.1 [पृष्ठ १७]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 9 Continuity
Exercise 9.1 | Q 10.2 | पृष्ठ १७

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