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Exercises relating to the integral test.

The function is decreasing for $x \geq \answer {N/A}$ (if the function is not ultimately decreasing, enter N/A). The integral test doesdoes not apply to the series The series convergesdivergescan’t be determined using this test .
The function is decreasing for $x \geq \answer {e}$ (if the function is not ultimately decreasing, enter N/A). The integral test doesdoes not apply to the series We have so the series convergesdivergescan’t be determined using this test .
The function is decreasing for $x \geq \answer {0}$ (if the function is not ultimately decreasing, enter N/A). The integral test doesdoes not apply to the series We have that so the series convergesdivergescan’t be determined using this test .
The integral test doesdoes not apply to the series The series convergesdivergescan’t be determined using this test .
Make a substitution $u = \ln x$.
The integral test doesdoes not apply to the series The series convergesdivergescan’t be determined using this test .
Make a substitution $u = \ln x$.
The integral test doesdoes not apply to the series The series convergesdivergescan’t be determined using this test .
The integral test doesdoes not apply to the series The series convergesdivergescan’t be determined using this test .
Make a substitution $u = x^2$ and then integrate by parts.
The function is decreasing for $x \geq \answer {1}$. By the integral test, We can approximate the infinite series by the sum of the first seven terms with what bounds on the error?
Write and then use the bounds we know for the “tail” (i.e., the sum over $n \geq 8$).
Using the integral test, we can determine that the sum of the series is equal togreater thanless than $2$.
Compare the series to the partial sum of the first three terms. Don’t forget to include an estimate of the remainder.

### Sample Quiz Questions

When approximating the sum of the infinite series by the sum of the first $N$ terms, how large must $N$ be to ensure that the approximation error is less than $1/200$? Choose the smallest correct bound among those listed.

$N > 5$ $N > 10$ $N > 20$ $N > 400$ $N > 8000$ $N > 160000$