The value of limx→∞ x3/2x3+1−x3−1 is

A
1
B
-1
C
0
D
none of these

Solution:

$\begin{matrix} x^{\frac{3}{2}} (\sqrt{x^{3} + 1} - \sqrt{x^{3} - 1}) = \frac{2 x^{\frac{3}{2}}}{\sqrt{x^{3} + 1} + \sqrt{x^{3} - 1}} \\ = \frac{2}{\sqrt{1 + \frac{1}{x^{3}}} + \sqrt{1 - \frac{1}{x^{3}}}} \to \frac{2}{1 + 1} = 1 as x \to \infty \end{matrix}$

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