question_answer

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

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

B)        \[-\frac{3}{8}{{x}^{2}}\]

C)        \[3x+\frac{3}{8}{{x}^{2}}\]          

D)        \[1-\frac{3}{8}{{x}^{2}}\]

Correct Answer: B

Solution :

Neglect the higher power ofin given expansion. \[\frac{{{(1+x)}^{3/2}}\,-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{1/2}}}\]  (neglect higher power of) (higher power ofgreater thancan be neglected)