## Calculus (3rd Edition)

The solution is $r=9.8696$.
We need to solve the inequality $| r - \pi^{2} | < 10^{-4}$. That is, we have $-10^{-4} \lt r - \pi^{2} \lt 10^{-4}$ $-10^{-4} + \pi^{2}\lt r \lt 10^{-4} + \pi^{2}$ We know that $\pi$ is not a rational number and neither is $\pi^2$. So, we can not take the solution $r = \pi^2$ between $-10^{-4} + \pi^{2}$ and $10^{-4} + \pi^{2}$. But, as a close estimation of a rational number to the irrational number $\pi^2$, we can choose $r=9.8696$. Thus, the solution is $r=9.8696$.