Today’s Quiz – a Second Chance

I  haven’t graded your quizzes yet, but I did flip through them to get a sense of how people were trying to answer the question. Many of you tried different methods, which can probably be made to work, but arrived at the wrong conclusion. A lot of your work also looks like it will be hard for me to follow as I search for partial credit. So…I’d like to make you an offer.

If you would like to rewrite your solution for today’s quiz question at home and hand it in at the beginning of class on Tuesday, I’ll grade that one instead of what you wrote today. (If you missed the quiz today, you can still hand in a quiz on Tuesday.) There is one serious condition however: there will be no partial credit awarded for the quizzes handed in on Tuesday; the only possible grades are 0/5 and 5/5, so if you decide to hand something in, everything needs to be perfect, explicit, and clear. (For example, even if you just miss the style point, then your grade will be 0/5.)

If you are handing in a paper on Tuesday, label it clearly with “Quiz #7 – Round 2” and your name at the top. No late papers will be accepted. The question is copied below.

Don’t forget: there is no class next Thursday, so no quiz next week; the following Tuesday you’ll have your third in-class test.

Quiz #7 – Round 2:

Determine whether the series converges absolutely, converges conditionally, or diverges:

\sum_{n=1}^\infty (-1)^n \frac{n^2 -n -1}{2n^2 + n +1}



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Test #3, this week’s quiz, and upcoming WebWork

Test #3 will be held in class on Tuesday, December 2.  It will cover sections 10.1-10.7. Because of the integral test, you may still need to apply techniques covered on the previous two tests.

This week’s quiz will cover sections 10.3-10.4.


Ratio and Root Tests due tomorrow night 11/19

Power Series due next Monday 11/24

Taylor Series due Monday 12/1


Just a reminder: no classes are scheduled for next Thursday 11/27.

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Upcoming WebWork

Due Monday, November 17: Convergence of Series with Positive Terms and Absolute and Conditional Convergence

Due Wednesday, November 19: Ratio and Root Tests

At the beginning of Tuesday’s class, we can talk about which ratio and root test exercises you’d like help with. By the way, after that, we’ll be finished with series where the individual terms are numbers and begin studying power series, which are like polynomials with infinitely many terms. The ratio test will come in handy for these as well.

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A not-hard-but-annoying thing

A couple times in class today I referred to something as not hard, but annoying. Here’s an example of the kind of thing I’m talking about:

Write the series \sum_{n=20}^\infty (2n+1) as an infinite series starting at n=0.

Notice that \sum_{n=20}^\infty (2n+1) = 2(20)+1 \; + \; 2(21)+1 \; + \; 2(22)+1 \; + \dots. In particular, we want our n=0 term to equal 2(20)+1, we want our n=1 term to equal 2(21)+1, and so on. So it might be helpful to view our series as 2(20+0)+1 \; + \; 2(20+1)+1 \; + \; 2(20+2)+1 \; + \dots. This would make general n term 2(20+n)+1.

So the series \sum_{n=20}^\infty (2n+1) can be rewritten as \sum_{n=0}^\infty (2(20+n)+1).

This actually isn’t brand new. Remember that if you have a function f(x) and you want to graph a new function g(x) = f(20+x), you just translate the graph of f(x) to the left 20 units. This also means that g(0) = f(20), g(1)=f(21), g(2)=f(22) and so on.

My own brain knows that these translations are possible, but it just can’t remember whether it’d have to add or subtract 20 in the above example, so it has to work harder than it wants to to figure out that it should add 20. This is why I called it “not hard, but annoying.” (It might look hard the first time you see it, but after you’ve worked through enough examples like the one above, you’ll find it’s actually easy and hopefully not too annoying for your brain.)

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WebWork and this week’s quiz

This Thursday’s quiz will cover sections 10.1 and/or 10.2.

The next two WebWork sets Convergence of Series with Positive Terms and Absolute and Conditional Convergence are both due Monday, November 17. I don’t want to freak anyone out, but I think these two sets will be challenging, so make sure you give yourself enough time to think about each of the exercises before the due date. If anyone has questions, I’m certainly happy to address them in class or during office hours, but now might be a good time to reach out to your classmates on the OpenLab too.

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WebWork and This Week’s Quiz

(1) The due date for the Sequences WebWork set has been updated. It’s now due tomorrow (Wednesday) night. Thanks for letting me know about the error.

(2) The WebWork set Summing an Infinite Series is due Monday, November 10. If you remember summation notation, most of the problems will be pretty easy for you. In fact, if you took Precalculus at CityTech, then you’ll be able to complete the set. We’ll discuss these topics (and others) in class on Thursday.

(3) I know how much you all love the Thursday quizzes, but this week’s quiz is cancelled. Focus instead on the material from 10.1 and 10.2 for your WebWork homework.

(4) Those of you who were assigned to the homework team for 10.1 may share your exercises on the board on Thursday.

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Test 2 and Midterm Grades

Test 2 grades and midterm grades are now available in Blackboard’s gradebook. Your midterm grade was calculated using the formula: test 1 and test 2: 40% each; quizzes and WebWork: 10% each. The midterm grade grade is for your information only. It won’t be submitted anywhere, but it should give you a reasonable idea of how you’re doing in the class.

The deadline to withdraw from the class is this Thursday, November 6.

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Test #2 Solutions


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Webwork – Taylor Polynomials Problem 3

If anyone is having trouble with this problem, I can help.

A couple questions to consider:

1. What is the definite integral of any function f(t) evaluated from 0 to 0?
2. What is the derivative below equal to, according to FTCII?:
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Quiz #5 – Thursday, October 23

This week’s material will cover material/problems from section 7.6 of your text (improper integrals).

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