मराठी

Lim X → 0 √ a 2 + X 2 − a X 2

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प्रश्न

\[\lim_{x \to 0} \frac{\sqrt{a^2 + x^2} - a}{x^2}\] 

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उत्तर

\[\lim_{x \to 0} \left[ \frac{\sqrt{a^2 + x^2} - a}{x^2} \right]\] 


On putting x = 0 in the expression  \[\sqrt{a^2 + x^2} - a\] it becomes \[\frac{0}{0} .\] Rationalising the numerator: 

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

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

=  \[\frac{1}{\sqrt{a^2} + a}\] 

=  \[\frac{1}{2a}\] 

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पाठ 29: Limits - Exercise 29.4 [पृष्ठ २८]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 29 Limits
Exercise 29.4 | Q 3 | पृष्ठ २८

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