Question

5. Which of the following is true regarding the following improper integral: \( \int_0^1 \frac{1}{(2 - x)^{1/2}} dx \) A. It converges to 1/3?2 B. It converges to 3?2/2 C. It converges to 3?2 D. It diverges E. None of the above 6. Find the arc length of the polar curve r = cos(?) + sin(?), 0 ? ? ? 2?. A. 2? B. 3?2? C. 4? D. ?2? E. 2?2? 7. Which of the following is true about the sequence: \( a_n = \left( 1 - \frac{9}{n} \right)^{n/3} \), n = 1, 2, 3, ... A. Converges to 1/e³ B. Converges to e³ C. Converges to e D. Converges to 1/e³ E. Diverges to ? 8. Compute the following limit: \( \lim_{n \to \infty} \frac{7^{n+1} + 2n^{100} + 75}{7^n + 3n^{100} - 99} \) A. 2/3 B. 7 C. 0 D. ? E. Does not exist

          5. Which of the following is true regarding the following improper integral: \( \int_0^1 \frac{1}{(2 - x)^{1/2}} dx \)
A. It converges to 1/3?2
B. It converges to 3?2/2
C. It converges to 3?2
D. It diverges
E. None of the above
6. Find the arc length of the polar curve r = cos(?) + sin(?), 0 ? ? ? 2?.
A. 2?
B. 3?2?
C. 4?
D. ?2?
E. 2?2?
7. Which of the following is true about the sequence:
\( a_n = \left( 1 - \frac{9}{n} \right)^{n/3} \), n = 1, 2, 3, ...
A. Converges to 1/e³
B. Converges to e³
C. Converges to e
D. Converges to 1/e³
E. Diverges to ?
8. Compute the following limit:
\( \lim_{n \to \infty} \frac{7^{n+1} + 2n^{100} + 75}{7^n + 3n^{100} - 99} \)
A. 2/3
B. 7
C. 0
D. ?
E. Does not exist

5. Which of the following is true regarding the following improper integral: ∫0^1 (1)/((2 - x)^1/2) dx
A. It converges to 1/3?2
B. It converges to 3?2/2
C. It converges to 3?2
D. It diverges
E. None of the above
6. Find the arc length of the polar curve r = cos(?) + sin(?), 0 ? ? ? 2?.
A. 2?
B. 3?2?
C. 4?
D. ?2?
E. 2?2?
7. Which of the following is true about the sequence:
an = ( 1 - (9)/(n))^n/3, n = 1, 2, 3, ...
A. Converges to 1/e³
B. Converges to e³
C. Converges to e
D. Converges to 1/e³
E. Diverges to ?
8. Compute the following limit:
limn →∞(7^n+1 + 2n^100 + 75)/(7^n + 3n^100 - 99)
A. 2/3
B. 7
C. 0
D. ?
E. Does not exist

Added by Kristine L.

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