Answer
a) 1.061, b) 1.0, c) 0.061
Work Step by Step
We are given: $f(x)=x^3-2x+3$
for $\delta f$ at 2:
$\delta f=f(2+0.1)-f(2)$
or $\delta f=(2.1)^3-2\times2.1+3-(2)^3-2\times2+3=8.061-7=1.061$
or $\delta f=1.061$
differentiation of f(x):
$f'(x)=3x^2-2$
$df=f'(2)\times0.1$
$df=(3\times2^2-2)\times0.1=1.0$
$df=1.0$
so
$|\delta f-df|=|1.061-1.0|=|0.061|=0.061$
The final answer is: a) 1.061, b) 1.0, c) 0.061