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Lim X → 0 √ 1 + X − 1 X is Equal to - Mathematics

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प्रश्न

\[\lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{x}\] is equal to 

विकल्प

  • \[\frac{1}{2}\] 

  • 2

  • 1

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उत्तर

\[\frac{1}{2}\] 

\[\lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{x}\]
\[ = \lim_{x \to 0} \frac{\left( \sqrt{1 + x} - 1 \right) \left( \sqrt{1 + x} + 1 \right)}{\left( \sqrt{1 + x} + 1 \right) x}\]
\[ = \lim_{x \to 0} \frac{1 + x - 1}{x\sqrt{1 + x + 1}}\]
\[ = \lim_{x \to 0} \frac{1}{x\left( \sqrt{1 + x} + 1 \right)}\]
\[ = \frac{1}{2}\]

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अध्याय 29: Limits - Exercise 29.13 [पृष्ठ ७९]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 29 Limits
Exercise 29.13 | Q 20 | पृष्ठ ७९

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