Question

Can you please find the limit and identify any vertical asymptotes of the function? Thanks

Answer 1

`\begin{gathered} \text{Given} \\ \lim_(x\rightarrow10)(1)/((x-10)^2) \end{gathered}`

Part A: Finding the limit

Find the left and right side of the limit.

`\begin{gathered} \lim_(x\to10^+)(1)/(\left(x - 10\right)^(2))=\infty \\ \lim_(x\to10^-)(1)/(\left(x - 10\right)^(2))=\infty \\ \\ \text{Since both sides approach the same value at }x=10,\text{ therefore} \\ \lim_(x \to 10) (1)/(\left(x - 10\right)^(2)) = \infty \end{gathered}`

Part B: Finding vertical asymptotes

At x = 10, x approaches infinity. therefore the vertical asymptote is x = 10.