QuestionFind the largest $\delta$ for $\lim _{x \rightarrow 2}\left(x^{3}-5 x+5\right)=3$ with $\varepsilon=0.2$ and $\varepsilon=0.1$. Round to four decimal places.

Studdy Solution
The largest possible value of $\delta$ for $\varepsilon=0.1$ is the maximum of the two $\delta$ values we found, which is $\delta=0.0959$.
So, the largest possible values of $\delta$ for $\varepsilon=0.$ and $\varepsilon=0.1$ are $\delta=0.192$ and $\delta=0.0959$, respectively.
$$\begin{array}{ll} \varepsilon=0. & \delta=0.192 \\ \varepsilon=0.1 & \delta=0.0959\end{array}$$