2. Compute the value of the following improper integral. If it is divergent, typ

Question

2. Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".

Answer:

Using the improper integral from above and the Integral Test, determine whether the following series converges or diverges. Answer "Converges" or "Diverges."

Answer: Converges or Diverges ?

3.   Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".

Answer:

Using the improper integral from above and the Integral Test, determine whether the following series converges or diverges. Answer "Converges" or "Diverges."

Answer: Converges or Diverges ?

Explanation / Answer

1) expression == > 1/(n^5 * (ln3)^5) [summantion from 0,infinity)

now as n increases the term goes to 0

hence converges

2) integral = 7*tan-1(x/3) [ 1, infinity]

= 7*(pi/2 - pi/6)

= 7 pi/3

so, such series will converge

3)let x^4 = t

so, dt = 4x^3 dx

so, integeral ==> integral (9/4 t^-1 dt) [4, infinity)

==> 9/16

such series will converge

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