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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

1 Answer

4 votes

Answer:

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.

User ColdCat
by
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