create a table of values for the function

Question

Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)

lim x→8 [x/(x + 1)] − (8/9)
x − 8
x	7.9	7.99	7.999	8.001	8.01	8.1
f(x)

Answer 1

(7.9,-7.89)

(7.99,-79.00)

(7.999,-790.11)

(8.001,790.13)

(8.01,79.02)

(8.1,7.9)

As you approach the value 8 from the positive and negative directions, they don't approach the same value, therefore the limit does not exist, or DNE.

If you graph it on the graphing calculator, you see that they don't approach the same value, it is a vertical asymptote.