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Final Exam

Final Exam. Remark : ( 24 ). Chapter10 Improper Integral Techniques of Integration. SUMMARY OF Power Series. 3) Binomial Series. 4) Taylor Series. 1) How to find Maclaurin series. Memorize. subsitute. differentiate. product. integrate. formula.

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Final Exam

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  1. Final Exam Remark: (24) • Chapter10 • Improper Integral • Techniques of Integration

  2. SUMMARY OF Power Series 3) Binomial Series 4) Taylor Series 1) How to find Maclaurin series Memorize subsitute differentiate product integrate formula 2) Find: radius and inteval of convergence Study the endpoints for interval of convergence 5) Applications of Power Series Find the sum Find integral

  3. MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620

  4. TERM-121

  5. TAYLOR AND MACLAURIN TERM-092

  6. TAYLOR AND MACLAURIN TERM-081

  7. TERM-121

  8. TERM-121

  9. SUMMARY OF TESTS Special Series: • Geometric Series • Harmonic Series • Telescoping Series • p-series • Alternating p-series P Series: Alter. P Series:

  10. SUMMARY OF TESTS Integral Test: Both convg or divg Series Tests Comparison Test: • Test for Divergence • Integral Test • Comparison Test • Limit Comparison Test • Ratio Test • Root Test • Alternating Series Test Smaller divg  bigger divg Bigger convg  Smaller convg Limit Comparison Test (1): Both convg or divg Limit Comparison Test (2): Ratio & Root

  11. SUMMARY OF TESTS 1) Determine whether convg or divg 2) Find the sum s 5-types 5) Partial sums 3) Estimate the sum s 4) How many terms are needed within error

  12. TERM-121

  13. TERM-121

  14. TERM-121 Alter. P Series:

  15. Ratio Test Root Test MIX easy to integrate Integral Test

  16. Alternating Series, Absolute and Conditional Convergence Absolutely convergent convergent THM: convg convg THM: conditionally convergent Absolutely convergent

  17. TERM-121

  18. TERM-091

  19. Recursively Defined Terms

  20. SERIES THEOREM: Convergent REMARK(2): Seq. series REMARK(3): Sequence convg convg

  21. TERM-121

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