Question

29) Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (1 point)limit of 1 divided by the quantity x minus 10 as x approaches 10 from the left

Answer 1

In order to find the limit and identify asymptotes, first let's write a table of ordered pairs (x, y) for the given expression:

`\begin{gathered} x=0\rightarrow y=-(1)/(10)\\ \\ x=5\rightarrow y=-(1)/(5)\\ \\ x=9.9\rightarrow y=-10\\ \\ x=10.1\rightarrow y=10\\ \\ x=15\rightarrow y=(1)/(5)\\ \\ x=20\rightarrow y=(1)/(10) \end{gathered}`

Graphing the points and the corresponding curve, we have:

We can see that there is a vertical asymptote at x = 10.

Also, the limit when x tends to 10-, that is, then x tends to 10 from the left, is equal to minus infinity.