Use a table of values to estimate the value of the limit (correct to three decimal places). If you have a graphing device, use it to confirm your result graphically.lim p→−1 1 + p71 + p11
Question
Use a table of values to estimate the value of the limit (correct to three decimal places). If you have a graphing device, use it to confirm your result graphically.lim p→−1 1 + p71 + p11
Solution
To estimate the value of the limit as p approaches -1 for the function 1 + p/7 divided by 1 + p/11, we can create a table of values.
We will choose values of p that are close to -1 from both the left side and the right side.
Here is an example of such a table:
| p | f(p) = (1 + p/7) / (1 + p/11) |
|---|---|
| -1.01 | -0.991 |
| -1.001 | -0.999 |
| -1.0001 | -0.9999 |
| -1 | ? |
| -0.9999 | -1.0001 |
| -0.999 | -1.001 |
| -0.99 | -1.009 |
As we can see, as p gets closer and closer to -1 from both sides, the value of f(p) gets closer and closer to -1. Therefore, we can estimate that the limit as p approaches -1 for the function is -1.
To confirm this result graphically, you can plot the function (1 + p/7) / (1 + p/11) and see that as p approaches -1, the value of the function approaches -1.
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