COMEDK · Maths · 16. Limits
\(\lim _\limits{x \rightarrow 0} \dfrac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}\) equals to
- A \(\dfrac{1}{2}\)
- B \(a^{-\dfrac{3}{2}}\)
- C \(2 a^{-\dfrac{3}{2}}\)
- D \(\dfrac{1}{2 a^{\dfrac{3}{2}}}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{1}{2 a^{\dfrac{3}{2}}}\)
Step-by-step Solution
Detailed explanation
Let the given limit be \(L = \lim_{x \rightarrow 0} \dfrac{\sqrt{a+x} - \sqrt{a}}{x \sqrt{a(a+x)}}\). Rationalizing the numerator by multiplying and dividing by \((\sqrt{a+x} + \sqrt{a})\):…
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