AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty}\left(\sqrt[3]{x^3+4 x^2}-\sqrt{x^2-3 x}\right)=\)
- A \(\frac{17}{6}\)
- B \(\frac{25}{6}\)
- C \(-\frac{1}{6}\)
- D \(\frac{37}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{17}{6}\)
Step-by-step Solution
Detailed explanation
\(\sqrt[3]{x^3+4 x^2} = x\left(1+\frac{4}{x}\right)^{1/3} = x\left(1+\frac{1}{3}\cdot\frac{4}{x} + \frac{\frac{1}{3}(-\frac{2}{3})}{2}\left(\frac{4}{x}\right)^2 + O(x^{-3})\right) = x+\frac{4}{3}-\frac{16}{9x} + O(x^{-2})\)…
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