Taylor/Maclauren Series

Today we learned about Taylor and Maclauren Series. A Maclauren series is a type of Taylor series where c(center) = 0. For now we have a basic formula for Taylor series that we start with for each problem. We found the Maclauren series for sin(x), cos(x) and e^x. Using these base functions we can easily find Maclauren series for similar functions such as sin(3x) or cos(x^2).

Today we began the last topic of the year by learning to write a rational function as a geometric series, using the Precalculus formula for the infinite sum of a converging geometric series. Using today's concept, we also learned about a series used to approximate pi.

Ratio Test

Yesterday (3/22) we started class with review, noting that if a series converges that means the sequences of partial sum converges. We also revisited the challenge problem which showed us with infinite series you can make the sum become almost whatever you'd like.

We then learned our final method of determining convergence: the Ratio Test.

And here is the other example we did:

Note: (n! + 1) / (n!) = n + 1

Alternating Series

March 9 - Pseries Test

The notes on the first part of the page deal with the worksheet that was handed out in class. Today, we learned about the Pseries test and its application to series and sequences.

feb 25. polar area problems

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!

Polar Arc Length

Yesterday in class, we learned how to find arc length in polar. To find polar arc length, we learned an equation that was similar to the one used to find the arc length in parametric equations. We also learned that when dr/d theta is positive, the distance from the pole is increasing, and when it is negative, the distance from the pole is decreasing.