Answer:
[tex]L(x)=4-x[/tex]
[tex]L(3.9)=0.1\\L(3.99)=0.01[/tex]
Step-by-step explanation:
The linear approximating polynomial is: [tex]L(x) = f(a) + f'(a)(x - a)[/tex]
Given: [tex]f(x) = 4 - x[/tex] at a=0
f(0)=4-0=4
f'(x)=-1, Therefore: f'(a)=-1
Therefore, the linear approximation of f(x) at a=0 is:
[tex]L(x) = f(0) + f'(a)(x - 0)\\L(x)=4-x[/tex]
We then use our result to approximate 3.9 and 3.99.
[tex]L(3.9)=4-3.9=0.1\\L(3.99)=4-3.99=0.01[/tex]
