MAT 1236 Calculus III Section 11.4 The Comparison Tests

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Presentation transcript:

MAT 1236 Calculus III Section 11.4 The Comparison Tests

HW …. WebAssign 11.4 Write out your solutions carefully And....

Come talk to me! If you are not 100% sure about... I am in my office MTR from 3 to 4:20 This is the first year in calculus III that no one come to ask me questions...

Reminder to Wai Do the first 3 examples on the board without erasing Overwrite on the first 3 examples to save time

Preview Comparison Test Limit Comparison Test Only work for series with positive terms Compare with standard series The nature of the comparison is term-by-term

Examples Comp. Test Limit Comp. Test

Examples Comp. Test Limit Comp. Test

How does it diverge?

The Comparison Test

Be Careful!!!!!

Example 1

Series to compare with

Remarks For convenience, we will call the following series a p-series. It has the same convergence as

Series to compare with

Example 1 Write down the general terms of the two series Write down the comparison and range Find the convergence of the comparison series Make the conclusion by quoting the name of the comparison test

Common Mistake/Misconception Comparing the series instead of comparing the terms The series are not comparable unless you first show that they are both convergent. The comparison test is based on the comparison of general terms. STOP

Examples Comp. Test Limit Comp. Test

Example 2 Remark: Need to justify the inequality if not obvious.

Examples Comp. Test Limit Comp. Test

Example 3

Examples Comp. Test Limit Comp. Test ?

The Limit Comparison Test (L.C.T.)

Example 4

Examples Comp. Test Limit Comp. Test ?

Example 5

Examples Comp. Test Limit Comp. Test ? ?

Example 6

Examples Comp. Test Limit Comp. Test ? ?