Answer
a) 0.41
b) 0.4
c) 0.01
Work Step by Step
We are given: $f(x)=x^2+2x$
for $\delta f$ at 0.1
$\delta f=f(1+0.1)-f(1)$
or $\delta f=1.1^2+2\times1.1-1-2\times 1=1.21+2.2-1-2=0.41$
or $\delta f=0.41$
differentiation of f(x):
$f'(x)=2x+2$
$df=f'(1)\times0.1$
$df=(2+2)\times0.1=0.4$
$df=0.4$
so
$|\delta f-df|=|0.41-0.4|=|0.01|=0.01$
The final answer is:
a) 0.41
b) 0.4
c) 0.01
