Ratio Test (continued from yesterday)

Today we learned about power series' centered at zero and applying the ratio test to these problems. Basically you're finding the x-values for which the ∑ converges. You have to pay attention to the type of ∑ you're looking at: geometric rules can apply here and save you some work. There are three possibilities of answers: 1) x=0; 2) x=all real numbers; 3) (-R,R).

polar area problems feb. 25

On Thursday , We covered polar area problems. We used geometry sketchpad to visualize the areas. By the end of this lesson you should be able to find the common area b/w function and the area inside of one function (outside the other function). We used the area integration formula in this lesson.
Things to remember: you must solve for each equation at the pole, you must be able to recognize when you have to set up 2 integrals, visualize first, make sure to find the point of intersection.

Hope it helps!

sorry this is so late.... two weeks ago in class we learned about probability. We learned about sample spaces and focused on probability using dice and cards.

We started class today by watching a Formula 1 Racing video, which was really cool but which also led to one of the topics we covered in class- velocity. We realized that it at one point in time, an object is not moving (think of a snapshot: in a picture, an object is stationary). The solution to that problem was the term instantaneous velocity.

In addition to this, we learned about finding the slope of the line tangent to a given graph at a certain point, also called the derivative, and finding the formula for the slope of a line tangent to a given graph at any point on the graph.

Limits with piecewise functions, One-sided limits, and More Algebra with Limits

We started class today by going over the homework from the night before (4/30). We then started talking about the limits of piecewise functions and one-sided limits, which is when you determine the limit of something by looking at it from either the positive or negative direction. This is indicated by having a + or - superscript. We then had more examples of algebra with limits.

More Limit Examples

 Today in class we went over more examples of limits. We focused mainly on how to approach the problem if  you get the fraction (0/0) when you first "plug in" the limit number.  If you do get (0/0) then you have to factor in order to cancel out like terms.  The "secret" that we learned today, was that you solve derivatives the same way you solve these limit problems. 

When a limit does not exist; Algebra and Limits; Direct Substitution

Today we learned that 3 reasons that a limit does not exist: the limit does not exist because of oscillating behavior; the limit does not exist because of unbounded behavior; the limit does not exist because of different left/right behavior.  We learned that algebra and limits is "nice" because it makes sense to us.  Direct substitution involves plugging the limit number into the equation.