Answer
a) $\frac{-1}{3}$
b) $\frac{-2}{5}$
c) $\frac{1}{15}$
Work Step by Step
We are given: $f(x)=x^{-1}$
$\delta f=f(0.5+0.1)-f(0.5)$
or $\delta f=f(0.6)-f(0.5)=0.6^{-1}-0.5^{-1}=\frac{5}{3}-2=\frac{-1}{3}$
or $\delta f=\frac{-1}{3}$
differentiation of f(x):
$f'(x)=-x^{-2}$
$df=f'(0.5)\times0.1$
$df=(-0.5^{-2})\times0.1=-0.4$
$df=-\frac{2}{5}$
so
$|\delta f-df|=|\frac{-1}{3}-\frac{-2}{5}|=|\frac{1}{15}|=\frac{1}{15}$
The final answer is: $a)\frac{-1}{3}, b)\frac{-2}{5}, c)\frac{1}{15}$
