Question

Complete the table. (Round your answers to four decimal places.)

[1/(x + 1)]- (1/9)
lim
X-8
7.9
7.99
7.999
D
8.001
8.01
8.1
2
Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.)
[1/(x+1)] - (1/9)
X-8

Answer 1

See below.

Explanation:

We have:

`\displaystyle \lim_(x\to \-8)\left((1)/(1+x)- (1)/(9)\right)`

Simply plug in each value:

When x = 7.9,
`\displaystyle (1)/(1+x)- (1)/(9) \approx 0.0012`

When x = 7.99,
`\displaystyle (1)/(1+x)- (1)/(9) \approx0.0001`

When x = 7.999,
`\displaystyle (1)/(1+x)- (1)/(9) \approx0.0000`

When x = 8.001,
`\displaystyle (1)/(1+x)- (1)/(9) \approx-0.0000`

When x = 8.01,
`\displaystyle (1)/(1+x)- (1)/(9) \approx-0.0001`

And when x = 8.1,
`\displaystyle (1)/(1+x)- (1)/(9) \approx-0.0012`

From this pattern, we can conclude that:

`\displaystyle \lim_(x\to \-8)\left((1)/(1+x)- (1)/(9)\right) = 0`

Since as the limit approaches 8, the value gets smaller and smaller and approaches zero.

Graphing this, we can confirm our answer.