#### Answer

a) 0.4641
b) 0.4
c) 0.0641

#### Work Step by Step

We are given: $f(x)=x^4$
$\delta f=f(1+0.1)-f(1)$
or $\delta f=f(1.1)-f(1)=1.1^4-1=1.4641-(1)=0.4641$
or $\delta f=0.4641$
differentiation of f(x):
$f'(x)=4x^3$
$df=f'(1)\times0.1$
$df=(4)\times0.1=0.4$
$df=0.4$
so
$|\delta f-df|=|0.4641-0.4|=|0.0641|=0.0641$
The final answer is: a)0.4641, b)0.4, c)0.0641