Up to this point in calculus and really every other math class you have probably taken, you have only been working within the rectangular coordinate system. This is the coordinate system in which you measure a horizontal distance (x) and a vertical distance (y) to create (x, y) coordinate points....

Previously in Calculus 2 (Lesson 7), we looked at how to use definite integrals to calculate the area of surfaces of revolution, which are formed by revolving a curve around either the x-axis or y-axis. Whenever we calculated the area of these surfaces of revolution, we always worked in terms of ...

Earlier in Calculus 2 (Lesson 6), we saw how to use a definite integral to calculate the arc length of a curve between two values of x. Up until now, we always calculated this arc length by working in terms of x because those curves had always been defined with functions in terms of x and y, or r...

In Calculus 1, we are introduced to the concept that a definite integral calculates the area under a curve between two values of x. Up to this point, the area that we wanted to calculate was beneath curves that were always defined with functions in terms of x and y, or rectangular equations. But ...

Another application of parametric derivatives is the ability to determine the concavity for plane/parametric curves. In fact, this is specifically an application of the second parametric derivative for a set of parametric equations.

You were first introduced to concavity in Calculus 1, where you...

One of the applications of parametric derivatives is the ability to determine the slope at a particular value of t (the parameter) along a plane/ parametric curve, and use that slope to find the equation of the tangent line for that value of t. This should be a familiar process, as finding slope ...

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 ...