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Let f be a continuous function with domain R. Assume fis POSITIVE and DECREASING. Assume lim f(z) = 0. Which of the following statements MUST be true? Select all the correct answers. (-1)" f(n) is divergent. IF f(z)dz is convergent, THEN [ f(n) is convergent. 100 n=1 nil (-1)" f(n) is convergent. WI SE f(n) is convergent. THEN f(z)dz is convergent.

Let f be a continuous function with domain R. Assume fis POSITIVE and DECREASING. Assume lim f(z) = 0. Which of the following statements MUST be true? Select all the correct answers. (-1)" f(n) is divergent. IF f(z)dz is convergent, THEN [ f(n) is convergent. 100 n=1 nil (-1)" f(n) is convergent. WI SE f(n) is convergent. THEN f(z)dz is convergent.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f be a continuous function with domain R. Assume fis POSITIVE and DECREASING. Assume lim f(x) = 0. Which of the following statements MUST be true? Select all the correct answers. 7L (-1)" f(n) is divergent. IF(z)dz is convergent, THEN Σf(n) is convergent. 100 n=1 n=1 (-1)" f(n) is convergent. IF F Σ f(n) is convergent. THEN f(x)da is convergent. 4
Transcribed Image Text:Let f be a continuous function with domain R. Assume fis POSITIVE and DECREASING. Assume lim f(x) = 0. Which of the following statements MUST be true? Select all the correct answers. 7L (-1)" f(n) is divergent. IF(z)dz is convergent, THEN Σf(n) is convergent. 100 n=1 n=1 (-1)" f(n) is convergent. IF F Σ f(n) is convergent. THEN f(x)da is convergent. 4
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