JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

\lim _{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:

View answer and explanation

Correct option: B

\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}

Option B (

\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}

) is correct because after applying L'Hopital's rule, the limit evaluates to

\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}

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