TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 3 / 2} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=\)
- A \(\sqrt[3]{3^{17}}\)
- B \(\sqrt[3]{3^{16}}\)
- C \(\sqrt[3]{3^{15}}\)
- D \(\sqrt[3]{3^{14}}\)
Answer & Solution
Correct Answer
(A) \(\sqrt[3]{3^{17}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow \frac{3}{2}} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{(2 x)^{1 / 3}-3^{1 / 3}} \\ & =\lim _{x \rightarrow \frac{3}{2}} \frac{2 x(2 x-3)\left(4 x^2+6 x+9\right)\left[(2 x)^{2 / 3}+3^{2 / 3}+(6 x)^{1 / 3}\right]}{(2…
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