Answer to Extra Credit Problem

Here's a one-stop for everyone needing detail on analysis. You can find the answer to the extra credit problem there as well as just about anything about mathematical analysis you want. I have a chalkboard at my house and can host some get-togethers for studying and analysis if you want. I think we could all benefit from it.

Alternatively, there's another approach offered from UC-Davis introduction to analysis course, of which our professor is an alumni. 

3.2 answers minus (35-45odd)

3.1 minus first and last problems (where'd they go?)

3.3 Answers 1-17 odd, 21-29 eeo with Thms (thm 3.5 is the most important)

Feel free to post answers on this post! I'm looking for your methods as well. I'd like to find the shorter path.  I write the theorems over and over for myself in order to learn them well enough to handle stress of testing.

Trig Skillz

The only trig id variations beyond the pythagorean id's in the homework problems assigned have been double angle formulas. Am I correct in reviewing that? Of course, you must know how to manipulate amplitude, period and shift, but I think that's part of the fundamentals and couldn't be covered as a form of review here. Double angles were covered briefly in my trig course, and they're the only ones I've seen in the problems. Here's my trig sheet that hangs by my table.

Trickster 1.5 problem

In order to use Thm 1.15, sin(x) must be converted to csc (x) as sin (0) = 0 and cannot be claimed as an infinite denominator while csc (0) = infinity and fits into Thm. 1.15. 

Likely 1.5 problem? With proof.

I think that's what she was getting at in class. I'm still weary of the non-graphical proof of the existence of the vertical asymptote, but this should do for the minimum work/maximum credit. I'm prepared for either case. 

Expected Form For 1.5 Questions?

Remember those points marked off for those simple limit equations we did on the first test? Well, let's not do that again. I think the form demonstrated here should be mimicked for the test. Just remember the qualification for one sided limits in the definition of infinite limits. It's a slight modification of the Epsilon-Delta definition, so it shouldn't be too difficult to memorize and evaluate. I hope you find this useful.

Test Review: Very Helpful Links For Test 2 (Updated at 17:41)

Test 2 covers 1.5 - 3.4. That's a lot of ground to cover, but I think we're all capable. For those of you not present, she emphasized theorem 1.15, the definition of vertical asymptote and theorem 1.14 as being on the test. That's a certainty. I'm not looking forward to doing the long math for those initial derivative equations. So easy to loose track of a sign or variable quantity. But do not fear!

You can spend countless hours seeking patterns in functions on this website. It helps see a pattern difference when we're manipulating polynomials. It's been fun graphing the individual factored intercepts to see the cumulative behavior of polynomials. But there's no time for that today!

https://www.desmos.com/calculator

At slader you can get a detailed step by step solving of the homework problems. Caveat! This book is 9th edition, but almost all of the problem prompts are identical erratum: not very much for chapter 3! but chapter 2 is great! . I hate the textbook industry. Such a waste of space. The theorems aren't listed, but some of the logical pathways towards a solution are. It's best to compliment this with memorized theorems and writing out the simplest logical path towards a solution that works for you. Remember, what she wants from us is to clearly demonstrate our utilization of the theorems to arrive at an answer. Be sure to do so while writing out your work. For slader.com, you'll need to set up an account to have access to the full solutions. It is very helpful.

http://www.slader.com/textbook/9780547167022-larson-calculus-9th-edition/

There is always www.calcchat.com. You can get some online help, though I haven't tried it. It is the simplest and most direct method for those of you that have taken Calculus before.

http://www.calcchat.com/

For video instruction there's ProfRobBob. He gets a little less clear as the concepts require more cross pollination from previous theorems, but I think our class adequately handles that. If you have a question about theorems of concepts, ask! It will provoke us to seek an adequate answer and to acknowledge our weaknesses. ProfrobBob, his alias for Mr. Tarrou, lightens the subject up a bit as he teaches a younger crowd in person, and therefore places less emphasis on the inherited knowledge that should already be readily available for this level of math. Problems with factoring? Trig? Just hop along his channel and you'll find whatever you need. 

https://www.youtube.com/user/profrobbob

This is Fikadu's favorite online youtube teacher. He truly helped me in simplifying derivatives involving rational exponents. I suggest you try him as well,

https://www.youtube.com/watch?v=IZzSvA8zBTY

This is a good video that helped me see quickly the relationship between f(x) and f prime (x) on the graph very quickly. I think it helps understand the tables we are working through in order to arrive at a few conclusions, and quickly. 

https://www.youtube.com/watch?v=CFu83NMl8lU

Good luck. I'm surprised no one has posted here yet, and that the class has been so quiet. I understand the intimidation of this course. Let's work together to keep up a great GPA so we can get to the destinations we want!

Mission Statement

1. In order to increase the overall test and quiz scores of the entire class, posts on this blog should demonstrate:

1. A step by step process of solving assigned homework
2. An accurate and clear demonstration of correct answers
3. If a correct answer isn't available for the student, it should be noted at the head of the post, as well as the troubles the assignment encountered by the student in executing them.
4. A list of applied theorems at the head of the problem with a reference to them throughout the executed problem.
5. Notes written by the student indicating pitfalls or troubles they had with the problem within the post of the executed problem.
6. Use pictures of your homework in order to post.

2. Collaboration among students:

1. Each post title should contain only the chapter and section number.
2. As homework isn't graded, academic honesty is not an issue here.
3. Share websites and tutorials that helped further your understanding with the appropriate section number to which the tutorial is applicable
4. Posts should be designated by volunteers prior to the blog using the email chain.
5. Address issues of clarity or correctness in the comments section.
6. Comments section should be used to discuss the topics related to the homework post or the given chapter and section title.
7. Check your work prior to posting at www.Calcchat.com 
8. Each student is responsible for their own work. This blog is a resource that is only as strong as your own working through problems and collaboration. Liability is the solely on the shoulders of the individual both outside and on this blog. This does not mean to not strive for your own accountability.

3. Posts beyond the scope of the text

1.  Should be limited.
2. Should further demonstrate problems addressed in the homework.
3. Should be posted with relative chapter and section number in the header.
4. Should relate to tutorials, textual demonstrations, or real world applications.

4. Be good to one another.

2.4 Answer Key With Theorem