[tex]\begin{gathered} \text{Given} \\ \lim_{x\rightarrow10}\frac{1}{(x-10)^2} \end{gathered}[/tex]
Part A: Finding the limit
Find the left and right side of the limit.
[tex]\begin{gathered} \lim_{x\to10^+}\frac{1}{\left(x - 10\right)^{2}}=\infty \\ \lim_{x\to10^-}\frac{1}{\left(x - 10\right)^{2}}=\infty \\ \\ \text{Since both sides approach the same value at }x=10,\text{ therefore} \\ \lim_{x \to 10} \frac{1}{\left(x - 10\right)^{2}} = \infty \end{gathered}[/tex]
Part B: Finding vertical asymptotes
At x = 10, x approaches infinity. therefore the vertical asymptote is x = 10.
