1. Determine whether the improper integral from 0 to 1, at 1 / (root x) dx conve

Question

1. Determine whether the improper integral from 0 to 1, at 1 / (root x) dx converges or diverges. If it converges, find what it converges to.

2. Determine whether the improper integral from 1 to ?, at xe^-x dx converges or diverges. If it converges, find what it converges to.

3. Determine whether the improper integral from 1 to 2, at 1/ (2x - 4)^2 dx converges or diverges. If it converges, find what it converges to.

4. Experiments show that the probability that a light bulb manufactured by a company will last a hundred hours is given by the integral from, a to ? at 0.012e ^-0.012t dt. In an interview, the CEO of the company says that 90% of the light bulbs manufactured by her company last at least 1000 hours. Would you characterize her statement as honest? Back up your answer with appropriate calculations and explanations.

5. Use the Comparison Theorem to determine whether the following improper integrals converge or diverge. Clearly state your answer, and justify your answer by writing a short proof.

(a) from 1 to ?, 1 /(x^ 5 + 1)dx

(b) from 1 to ?, at (x + sin^2 x)/ (x^ 2) dx

6. Determine whether each of the following sequences converge or diverge. Clearly state your answers. If they converge, find what they converge to.

(a) [n / 1 + (root n) ] at ? n=1

(b) [(sin^2 n) /4n ]at ? n=1

(c) [(e ^2n)/ (2n + e^ 2n)] at ? n=1

(d) [(ne^ (- root n))] at ? n=1

Need to answer these questions please show work!

? mark is infinity

Will rate the best answer 5 stars!

Explanation / Answer

not able to vie thw q pl share & rate

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.