If x is so small that x³ and higher powers of x may be neglected, then ((1 + x)^(3/2) - (1 + 1/2x)³)/((1 - x)^(1/2)) may be approximated as

Binomial Theorem and Its Simple Applications: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q2961

JEE Main 2005Annual, Paper 1MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

x

is so small that

{x^3}

and higher powers of

x

may be neglected, then

{{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}}

may be approximated as