APFIVE Limit Of A Riemann Sum For An Improper Integral
| $$n$$ | $$\displaystyle \sum_{k=1}^{n} \left(\frac{1}{x_k}\right)\left(\frac{1}{n}\right)$$ |
|---|---|
| 100 | 5.19 |
| 200 | 5.88 |
| 300 | 6.28 |
| 400 | 6.57 |
| 500 | 6.79 |
The table above shows several Riemann sum approximations to $$\displaystyle \int_0^1 \frac{1}{x} dx$$ using right-hand endpoints of $$n$$ subintervals of equal length of the interval $$[0, 1]$$. Which of the following statements best describes the limit of the Riemann sums as $$n$$ approaches infinity?
A
The limit of the Riemann sums is a finite number greater than 10.
B
The limit of the Riemann sums does not exist because it is a sum of infinitely many positive numbers.
C
The limit of the Riemann sums does not exist because $$\displaystyle \int_0^1 \frac{1}{x} dx$$ does not exist.
D
The limit of the Riemann sums is a finite number less than 10.
Question Leaderboard
Not enough data yet to show leaderboard.