Week #3
You should be finished with the limit law problems in Stewart's textbook, and we'll move forward from here, but you better have limits under control before moving on.
I realize that I put up the assignment during the quiz, and many may have missed it, so here it is: Section 2.3 , Problems: 11 - 29 odd, 33, 37 - 47 odd, optional 51, optional 59.
As for quiz number 1, it was a near disaster (score = 1) for some, easy as pie (score = 10) for others. Most depressing, is that many of you cannot evaluate a function (second problem) using a calculator! The function problem (first problem) may have appeared to be new, but it was pretty easy algebra. Solutions to this quiz are posted on this blog --- just look at the section under "Course Files", it's to your right. You should be prepared to stretch your brains on occasion. Please post comments, especially if you have something constructive to say, or you just want to share your frustrations/elations.
Okay, so this week we'll probably do the precise definition of the limit, continuity, and then finish off chapter 2, including finishing the Squeeze Theorem. Then it's onto the meat of calculus, THE DERIVATIVE AND ITS APPLICATIONS.
I realize that I put up the assignment during the quiz, and many may have missed it, so here it is: Section 2.3 , Problems: 11 - 29 odd, 33, 37 - 47 odd, optional 51, optional 59.
As for quiz number 1, it was a near disaster (score = 1) for some, easy as pie (score = 10) for others. Most depressing, is that many of you cannot evaluate a function (second problem) using a calculator! The function problem (first problem) may have appeared to be new, but it was pretty easy algebra. Solutions to this quiz are posted on this blog --- just look at the section under "Course Files", it's to your right. You should be prepared to stretch your brains on occasion. Please post comments, especially if you have something constructive to say, or you just want to share your frustrations/elations.
Okay, so this week we'll probably do the precise definition of the limit, continuity, and then finish off chapter 2, including finishing the Squeeze Theorem. Then it's onto the meat of calculus, THE DERIVATIVE AND ITS APPLICATIONS.
posted by Ron Bannon at
9/16/2004 08:38:00 PM
4 Comments:
For one, use radian mode, otherwise you will get an incorrect answer. You should also be aware that radians are unit-less and physically make sense.
The term radian arises from the fact that the length of a circular arc (usually denoted S), corresponding to an angle of one (1) radian, is equal to the radius (usually denoted r) of the arc. The relationship you were taught in MTH 120 was that: (arc length) = (radius) * (angle in radians). The radian is used by mathematicians, and anyone else interested in using mathematics to model natural phenomena. Radian is a (SI) Standard International unit for angular measure.
If I were a dictator, I would forbid the use of the word degree in reference to angles, except in the privacy of one's home.
From Petr Beckmann's "A History of Pi" . . .
"In 1936, a tablet was excavated some 200 miles from Babylon. Here one should make the interjection that the Sumerians were first to make one of man's greatest inventions, namely, writing; through written communication, knowledge could be passed from one person to others, and from one generation to the next and future ones. They impressed their cuneiform (wedge-shaped) script on soft clay tablets with a stylus, and the tablets were then hardened in the sun. The mentioned tablet, whose translation was partially published only in 1950, is devoted to various geometrical figures, and states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60 + 36/(60^2) (the Babylonians used the sexagesimal system, i.e., their base was 60 rather than 10).
The Babylonians knew, of course, that the perimeter of a hexagon is exactly equal to six times the radius of the circumscribed circle, in fact that was evidently the reason why they chose to divide the circle into 360 degrees (and we are still burdened with that figure to this day). The tablet, therefore, gives ... Pi = 25/8 = 3.125."
By
Ron Bannon, at 9:18 PM
The school (ECC) has a site license for Mathematica, and I believe it's available in the 3100 labs. You should see the Mathematica icon on the desktop of these machines, just double click, and type . . .
Limit[x/Tan[x], x -> Pi/2, Direction -> -1]
. . . then you'll get the result. What's this? Take a look at quiz 1.
You can stop by my office if you have any questions.
By
Ron Bannon, at 7:54 PM
I placed a new link on the right, and it will take you to Wolfram's -- the developer of Mathematica -- home page.
By
Ron Bannon, at 8:08 PM
What, afraid of \LaTeX{}? Well, stop by my office and I think as long as you're registered at ECC, I can give you the licnese number for the full version. Download a copy of MathType, which includes Equation Editor, and the license number for ECC will activate your copy into a full working version. I have the license number of Mac OS X, but I can probably dig one up for Windows :-) too.
By
Ron Bannon, at 8:36 PM
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