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Calculus BC Help - Series
6. Let f be the function defined by f(x)=1x2+9.

(a) Evaluate the improper integral ∫∞3f(x) dx, or show that the integral diverges.
(b) Determine whether the series ∑n=3∞f(n) converges or diverges. State the conditions of the test used for determining convergence or divergence.
(c) Determine whether the series ∑n=1∞(−1)n(en⋅f(n))=∑n=1∞(−1)n(n2+9)en converges absolutely, converges conditionally, or diverges.

Calculus BC Help Series 6 Let f be the function defined by fx1x29 a Evaluate the improper integral 3fx dx or show that the integral diverges b Determine whether class=
Calculus BC Help Series 6 Let f be the function defined by fx1x29 a Evaluate the improper integral 3fx dx or show that the integral diverges b Determine whether class=
Calculus BC Help Series 6 Let f be the function defined by fx1x29 a Evaluate the improper integral 3fx dx or show that the integral diverges b Determine whether class=

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jesusm1

Answer:

  1. So you have a power of x^2, notice if you have a harmonic series, or if it looks familiar, which it should, hint (1/x)
  2. Now integrate:
  3. let u= x/3 dx=3du
  4. now integral (1/u^2+1)
  5. recognize thats arc
  6. so you get a result of: arctan(x/3)/3+c

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