Blog #1--Stephen Ledbetter

Okay, so this is my first blog for this year in AP Calc. I must say that the whole site looks kinda different than last year...it looks good. So, we started AP Calculus this year, and for the past two weeks we've been doing nothing but limits. Limits limits limits! But we're almost done with 'em. Limits are easy if you know how to do all the "stuff" necessary to "solve" them. And these last two weeks have been just a basic review of the last part of Advanced Math last year (Pre-Calculus). Anyway, let me get to the actual math part of the blog :/

I'll explain in my own words how to solve a limit with a zero in the denominator by way of making a chart.

If you happen to come across a limit problem where the denominator equals 0, you can make a chart to find the limit as x approaches a said number from the left and right sides of the graph (number that x approaches).

You use the values of 0.001, 0.01, and 0.1 to determine these values.

On the left side, (from left to right) the values would be (number - .1, # - .01, # .001). On the right side (from left to right) the values would be (number + .001, # + .01, # + .1).

You plug the equation of the limit into y= on your calculator, then plug the decimal values into the x values on the table. (If you plug in the actual number that x approaches, you should see "ERROR" on the table.)

Then, you just see what the limit is approaching from the left (left to right) to the median number, and then what the limit is approaching from the right (right to left) to the median number. If they match, that is the limit. If they don't, then it is said it does not exist (DNE).

Example:

the limit as x approaches 4 of ((1)/(x-4))

You plug the equation into the calculator.

Now plug in

3.9 = -10

3.99 = -100

3.999 = -1000

4 = ERROR

4.001 = 1000

4.01 = 100

4.1 = 10

You can see that as x approaches 4 from the left, the limit is (negative)infinity.

As x approaches 4 from the right, the limit is infinity.

They do not match, therefore the limit does not exist (DNE).

I really don't understand how to discuss continuity. I'm still a little iffy on removables and jumps and I can't seem to grasp the concept of them. Maybe a definition and a couple of examples of them could help. Thanks.