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IMPROPER INTEGRALS

IMPROPER INTEGRALS. THE COMPARISON TESTS. In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST). convg. Known Series. Example:. Determine whether the series converges or diverges. geometric.

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IMPROPER INTEGRALS

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  1. IMPROPER INTEGRALS

  2. THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) convg Known Series Example: Determine whether the series converges or diverges. geometric P-series

  3. THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) divg Known Series Example: Determine whether the series converges or diverges. geometric P-series

  4. THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) convg THEOREM: (THE COMPARISON TEST) divg

  5. THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-112

  6. THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) divg Example: Determine whether the series converges or diverges.

  7. THE COMPARISON TESTS THEOREM: (THE LIMIT COMPARISON TEST) both series converge or both diverge. With positive terms Example: Determine whether the series converges or diverges.

  8. THE COMPARISON TESTS THEOREM: (THE LIMIT COMPARISON TEST) both series converge or both diverge. and Converge, then convg With positive terms and divg, then divg Example: Example: Determine whether the series converges or diverges. Determine whether the series converges or diverges. REMARK: Notice that in testing many series we find a suitable comparison series by keeping only the highest powers in the numerator and denominator.

  9. THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-112

  10. THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-111

  11. THE COMPARISON TESTS Remarks: convg

  12. THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-092

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