When working with plane/ parametric curves, it may sometimes be of interest to know the slope at a particular point along that curve. We learn in Calc 1 that the slope at a point along a curve/function is represented by the derivative of that function, and we have a whole arsenal of different dif...

In the last lesson we completed the second major group of concepts in Calculus 2, which was sequences and series. With the conclusion of those concepts, we are now ready to begin the third and final major group of concepts in Calc 2, which is parametric equations and polar coordinates. 

We will ...

In a previous lesson we established two special types of power series known as Taylor series and Maclaurin series. One of the applications of these series is the ability to approximate the value of a function at a particular value of x. This is done by using what are known as Taylor polynomials, ...

In the last lesson we introduced two new types of power series known as Taylor series and Maclaurin series. Many functions can be represented as power series by forming Taylor series or Maclaurin series for those functions. However, there is a specific type of function that when represented as a ...

In the past few lessons we have focused on power series, and how we can represent functions as a power series. Specifically, we were representing functions similar to the form of the sum of a geometric series as a power series. However, this is not the only way to represent a function as a power ...

In the previous lesson we saw how functions that are similar to the form of the sum of a geometric series can be represented with a power series. However, we can extend this idea to more functions. Specifically, we can represent functions whose derivative or integral is similar to that form of a ...

So far we have seen that power series create functions that are defined for a domain of x values for which the power series is convergent. However, can we actually take a specific function and express it as a power series? Well, there's actually several methods for rewriting functions as power se...

Previously we established that a power series creates a function that is defined for the values of x for which the power series is convergent. Well since a power series is a function, we are naturally interested in knowing its derivative and integral (antiderivative). To find each of these functi...

A power series is a special type of series that involves a variable, usually x, raised to some power of n. As such, each of the terms of a power series involve x, and as a result, form a function f(x). However, this function is not any normal function, it is a function that is only defined for th...

One more method we can use to test for the convergence or divergence of a series is what is known as the Root Test. This test will be particularly useful for series that involve powers of n.

The Root Test involves evaluating the limit of the nth root of the absolute value of the nth term of a se...