Question

If $x$ be so small that its square and higher powers may be neglected, find the value of :
$(1-7x{)}^{\frac{1}{3}}(1+2x{)}^{-\frac{3}{4}}$

Answer 1

let

$y=(1-7x{)}^{\frac{1}{3}}(1+2x{)}^{\frac{-3}{4}}$

$=(1-\frac{1}{3}.7x-\frac{2}{9}\frac{49x^2}{2!}.....)(1-\frac{3}{4}.2x+\frac{21}{16}\frac{4x^2}{2!}...)$

x be so small that its square and higher powers may be neglected

$=(1-\frac{1}{3}.7x)(1-\frac{3}{2}.x)$

again neglect square terms

$=1-\frac{23x}{6}$