Limiting the discussion

June 10, 2006

A message last night from a friend pointed out that this chapter may contain too much and might be unfocused. It was a great suggestion. I had just sent a note off to my editor saying that I had decided that chapter two would be about limits and that continuity would now become chapter three.

The down side is that this seems to extend the discussion of these two topics while the student is raring to go and wants to get to the good stuff. As they will later learn, however, this is the good stuff. So many of the theorems require an understanding of these two topics. The one I was tempted to give short shrift to is continuity – we’ll see.

As for limits, I’m leaving the formal definition until the end of the chapter. This means that I’m not providing formal proofs of any of the limit theorems. That may be ok. I want students to understand that if the limit as x -> a f(x) = 7 then lim x->a [f(x) + 3] is 10. I’ve seen tons of students who know the limit of the sum is the sum of the limits when they are studying that section of the book – can we get them to grasp these theorems at a gut level.

It also sets up nicely the expectation that the derivative of the product is the product of the derivatives.


8 Responses to “Limiting the discussion”

  1. charlie angevine Says:

    You must have had a long week; in the final paragraph you typed product twice where you meant to say sum.

    In the calc books I’ve used all a student really needs to know about continuity is that they can draw a continuous function without lifting their pencil. Of course these books never try to prove theorems.

    I am so glad you are back to work on the book. I can’t tell you how excited I am about the prospect of a head first calculus book. If you would like an enthusiastic reviewer/typo-hunter/problem-checker I am willing.

  2. Pyracantha Says:

    Dear sir: I am a 53-year-old commercial artist and I am just learning calculus for the first time, on my own using books, along with some help from my math and science friends. Six years ago after a sort of “conversion experience” I decided to learn mathematics and physics, which I never learned in my high school or college days. You do not leave a private e-mail contact anywhere so I will give my Website address for you to look at. My Weblog, ELECTRON BLUE (scroll down to bottom of “index” page) is my journal of how an artist learns mathematics and physics. You may be interested in it. My site is at http://www. I am looking forward to your calculus text, I will still be learning it when it is published.

    Yours, Pyracantha

  3. Franje Says:

    You haven’t blogged in some time. Are you alright? I hope you are fine.

  4. Kisakookoo Says:

    Hi! Why I can’t fill my info in profile? Can somebody help me?
    My login is Kisakookoo!

  5. SamyIsocacy Says:

    Two new studies show why some people are more attractive for members of the opposite sex than others.

    The University of Florida, Florida State University found that physically attractive people almost instantly attract the attention of the interlocutor, sobesednitsy with them, literally, it is difficult to make eye. This conclusion was reached by a series of psychological experiments, which were determined by the people who believe in sending the first seconds after the acquaintance. Here, a curious feature: single, unmarried experimental preferred to look at the guys, beauty opposite sex, and family, people most often by representatives of their sex.

    The authors believe that this feature developed a behavior as a result of the evolution: a man trying to find a decent pair to acquire offspring. If this is resolved, he wondered potential rivals. Detailed information about this magazine will be published Journal of Personality and Social Psychology.

    In turn, a joint study of the Rockefeller University, Rockefeller University and Duke University, Duke University in North Carolina revealed that women are perceived differently by men smell. During experiments studied the perception of women one of the ingredients of male pheromone-androstenona smell, which is contained in urine or sweat.

    The results were startling: women are part of this repugnant odor, and the other part is very attractive, resembling the smell of vanilla, and the third group have not felt any smell. The authors argue that the reason is that the differences in the receptor responsible for the olfactory system, from different people are different.

    It has long been proven that mammals (including human) odor is one way of attracting the attention of representatives of the opposite sex. A detailed article about the journal Nature will publish.

  6. Idetrorce Says:

    very interesting, but I don’t agree with you

  7. meraslees Says:

    Good viagras
    πŸ™‚ When you go online to order Levitra (also sold under the generic name Vardenafil), you will find so many online pharmacies (OPs) to choose from. How do you know which ones are safe?
    Bye !!

  8. Doiy Says:

    I agree. πŸ˜‰

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: