Use a calculator estimate the given limit. \( \lim _{x \rightarrow 3} \frac{5}{(x-3)^{2}} \)

To estimate the limit \( \lim _{x \rightarrow 3} \frac{5}{(x-3)^{2}} \) using a calculator, try substituting values of \( x \) that are very close to 3, for example, 2.9 and 3.1. When you substitute \( x = 2.9 \): \[ \frac{5}{(2.9 - 3)^{2}} = \frac{5}{(-0.1)^{2}} = \frac{5}{0.01} = 500. \] And when substituting \( x = 3.1 \): \[ \frac{5}{(3.1 - 3)^{2}} = \frac{5}{(0.1)^{2}} = \frac{5}{0.01} = 500. \] As \( x \) approaches 3, the function approaches very large values, indicating that the limit is \( \infty \).