Chapter 11.3, Problem 41E

Solution

To find: $\underset{x\to 2^{+}}{\lim }\mathrm{int}\left(x\right)$

  $\underset{x\to 2^{+}}{\lim }\mathrm{int}\left(x\right)=2$

Given information:

  $\underset{x\to 2^{+}}{\lim }\mathrm{int}\left(x\right)=2$

Calculation:

As $x$ approaches $2$ from the right, the greatest integer of the limit of the function is $2$ .

Therefore,

  $\begin{array}{l}\underset{x\to 2^{+}}{\lim }f\left(x\right)=\underset{x\to 2^{+}}{\lim }\mathrm{int}\left(x\right)\\ =2\end{array}$

Hence, the greatest integer contained in $\underset{x\to 2^{+}}{\lim }\mathrm{int}\left(x\right)=2$ .