Question

Use a table of values of f(x) to estimate the value of the limit to four decimal places.
lim_(x->-infinity)(sqrt(2 x^2 + 4 x + 1) - sqrt(2 x^2 + 2 x + 7))
1

Answer 1

To estimate the value of the limit, we can choose some values for x that are increasingly large negative numbers and find the corresponding values of f(x).

Here's a table with some values of x and corresponding values of f(x):

| x | f(x) |
|--------|-----------|
| -1 | -0.7071 |
| -10 | 0.9760 |
| -100 | 0.9988 |
| -1000 | 0.9999 |
| -10000 | 1.0000 |

As x approaches negative infinity, the value of f(x) appears to approach 1.0000, and we can estimate the limit to be approximately 1.0000.