QuestionFind $\delta$ such that if $|x-1|<\delta$, then $|f(x)-1|<0.2$, given $f(1)=1$, $f(1.1)=0.8$, $f(1.2)=1.2$.

Studdy Solution
The distance between $1$ and $1.1$ is $0.1$ and the distance between $1$ and $1.2$ is $0.2$. Therefore, we choose $\delta$ to be the smaller of these two distances, which is $0.1$.
So, $\delta =0.1$.
With this choice of $\delta$, if $|x-1|<\delta$ then $|f(x)-1|<0.2$.