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Lim X → 0 Sin 3 X + 7 X 4 X + Sin 2 Xv - Mathematics

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प्रश्न

\[\lim_{x \to 0} \frac{\sin 3x + 7x}{4x + \sin 2x}\]

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उत्तर

\[\lim_{x \to 0} \left[ \frac{\sin 3x + 7x}{4x + \sin 2x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\frac{\sin 3x}{3x} \times 3x + 7x}{4x + \frac{\sin 2x}{2x} \times 2x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\left( \frac{\sin 3x}{3x} \times 3 + 7 \right)x}{\left( 4 + \frac{\sin 2x}{2x} \times 2 \right)x} \right]\]
\[ = \frac{3 + 7}{4 + 2}\]
\[ = \frac{10}{6} = \frac{5}{3}\]

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अध्याय 29: Limits - Exercise 29.7 [पृष्ठ ५१]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 29 Limits
Exercise 29.7 | Q 54 | पृष्ठ ५१

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