Mary Graci - Blog #1

Hey, this is Mary Graci. We’ve finally started the new year and now we’re in Calculus. To summarize these first two weeks, we’ve pretty much just reviewed what we learned at the end of the year in Adv. Math last year. But anyway, that review was of limits. We first re-learned how to create tables when the limit has a zero in the denominator. An example from our homework:

Ex. 1) lim as x approaches 2 ((x-2)/(x^2-4))
First, created a table by subtracting .1, .01, and .001 from 2, and adding .001, .01, and .1 to 2. Then plug those numbers into the equation. In this case, the answers are 100, 10000, 1000000, and 1000000, 10000, 100. Now compare both sides of the table and determine what each side is approaching, and obviously both sides are approaching infinity. So, from this you get infinity as your limit.

Next, we learned how to solve limits numerically without a chart, when there isn’t a zero in the demoninator. (It also happens to be the easiest way to solve limits!) All you have to do is plug in the x value given into the equation and, as easy as can be, you get the limit! But, an example anyway:

Ex. 2) lim as x approaches -3 (3x+2) = -7

Another problem may involve a trig function, but essentially, it works the same way.

Ex. 3) lim as x approaches 1 (cos pi x /3) = cos pi/3 = ½
**hint: don’t forget your trig chart!!!

There are, however, two special trig limits:
1) lim as x approaches 0 (sin x/x) = 1
2) lim as x approaches 0 (1-cos x/x) = 0

Besides solving limits numerically, you can also use algebra (factoring out discontinuities to make the problem simpler and then plugging in the x value to get the limit) and graphing (plugging the equation into your calculator, looking at the graph, and figuring out the limit that way.)

Besides that, I basically understood everything this week. It was all pretty easy and I did pretty good on the quizzes (especially the one Friday!) I don’t really have any questions this week, but I know it’s just going to get harder from here on out.