If x is so small that \[{{x}^{3}}\] and higher powers of x may be neglected, then \[\frac{{{(1+x)}^{\frac{3}{2}}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{\frac{1}{2}}}}\] may be approximated as [AIEEE 2005]

\[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\]

If x is so small that \[{{x}^{3}}\] and higher powers of x may be negl

1.	If x is so small that \[{{x}^{3}}\] and higher powers of x may be neglected, then \[\frac{{{(1+x)}^{\frac{3}{2}}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{\frac{1}{2}}}}\] may be approximated as [AIEEE 2005]
A.	\[-\frac{3}{8}{{x}^{2}}\]
B.	\[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\]
C.	\[1-\frac{3}{8}{{x}^{2}}\]
D.	\[3x+\frac{3}{8}{{x}^{2}}\]
Answer» B. \[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\]

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If x is so small that \[{{x}^{3}}\] and higher powers of x may be neglected, then \[\frac{{{(1+x)}^{\frac{3}{2}}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{\frac{1}{2}}}}\] may be approximated as [AIEEE 2005]

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