Final Exam Term121Term112 Improper Integral and Ch10 16 Others 12 Term121Term112 Others (Techniques of Integrations) 88 Others-Others 44 Remark: ( 24 )

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Presentation transcript:

Final Exam Term121Term112 Improper Integral and Ch10 16 Others 12 Term121Term112 Others (Techniques of Integrations) 88 Others-Others 44 Remark: ( 24 ) 1)Chapter10 2)Improper Integral 3) Techniques of Integration

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

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

TERM-121

TAYLOR AND MACLAURIN TERM-092

TAYLOR AND MACLAURIN TERM-081

TERM-121

Special Series: 1)Geometric Series 2)Harmonic Series 3)Telescoping Series 4)p-series 5)Alternating p-series SUMMARY OF TESTS P Series: Alter. P Series:

Series Tests 1)Test for Divergence 2) Integral Test 3) Comparison Test 4) Limit Comparison Test 5) Ratio Test 6)Root Test 7)Alternating Series Test SUMMARY OF TESTS Integral Test: Both convg or divg Comparison Test: Smaller divg  bigger divg Bigger convg  Smaller convg Limit Comparison Test (1): Both convg or divg Limit Comparison Test (2): Ratio & Root

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

TERM-121

Alter. P Series:

Ratio Test Root Test MIX easy to integrate Integral Test Faster

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

TERM-121

TERM-091

Recursively Defined Terms

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

TERM-121