JEE Mains · Maths · STD 11 - 12. limits
\(\lim \limits_{x \rightarrow a} \frac{(a+2 x)^{\frac{1}{3}}-(3 x)^{\frac{1}{3}}}{(3 a+x)^{\frac{1}{3}}-(4 x)^{\frac{1}{3}}}(a \neq 0)\) is equal to
- A \(\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}\)
- B \(\left(\frac{2}{3}\right)^{\frac{4}{3}}\)
- C \(\left(\frac{2}{9}\right)^{\frac{4}{3}}\)
- D \(\left(\frac{2}{9}\right)\left(\frac{2}{3}\right)^{\frac{1}{3}}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}\)
Step-by-step Solution
Detailed explanation
Required limit \( L =\lim _{h \rightarrow 0} \frac{(a+2(a+h))^{1 / 3}-(3(a+h))^{1 / 3}}{(3 a+a+h)^{1 / 3}-(4(a+h))^{1 / 3}} \)…
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