Question

The approximate value of $(0.007{)}^{13}$

• A. $\frac{23}{120}$
• B. $\frac{27}{120}$
• C. $\frac{19}{120}$
• D. $\frac{17}{120}$

Answer 1

Answer: (A)

Let $f(x)=x^{1/3}$
$\Rightarrow f^{\prime }(x)=\frac{1}{3}{x}^{-2/3}$
Now $f(x+\Delta x)-f(x)=f^{\prime }(x)\cdot \Delta x=\frac{\Delta x}{3\left(x^{2/3}\right)}$
We may write, $0.007=0.008-0.001$,
taking. $x=0.008$ and $dx$ $=-0.001$
we have $f(0.007)-f(0.008)=-\frac{0.001}{3(0.008{)}^{2/3}}$
$\Rightarrow f(0.007)-(0.008{)}^{1/3}=-\frac{0.001}{3(0.2{)}^2}$
$\Rightarrow f(0.007)=0.2-\frac{0.001}{3(0.04)}$
$=0.2-\frac{1}{120}=\frac{23}{120}$
Hence $(0.007{)}^{1/3}=\frac{23}{120}$