The three week Calculus Study Group (4) uses the Introduction to Calculus self study course as part of the daily lectures and covers functions, limits, differential calculus, and integral calculus. This course is a good way to prepare for AP Calculus and is a great refresher on the topic.

The functions 3^x, the derivative of 3^x, e^x, the derivative of e^x, and 2^x, the derivative of 2^x are shown in the plot on the left in the figure below to show the awesome properties of e^x, for example. The derivative of e^x is e^x so the slope anywhere on the line is just the value of the function at that point.

The tangent line and normal line are shown in the plot on the right for e^x=3. This point was chosen as an example. The functions used to create the tangent and normal lines are as follows.

• f(x)=e^x
• Tangent(x)=f′(x)(x−x0)+f(x0) at x0=3
• Normal(x)=(−1/f′(x))(x−x0)+f(x0) at x0=3

The area under e^x to x0=3 can be found by integrating the curve from −∞ to 3 and is e³. Thus, the area under the curve is also the value of the function at that point.

To receive a program completion certificate you must pass three quizzes.