Derivative of e^x

Today we talked about the derivative of exponential functions (e^x). We found out that the derivative of e^x is the same as the function (e^x). We then did examples to apply the different properties of exponential functions and derivatives.

The Derivative of ln(x)!!

Today, we calculated that the derivative of ln(x) is (1/x), and applied it to several problems, incorporating logarithmic ideas AND the chain and product rules!

Classnotes- 11/02/10

Today in class we discussed how to solve complicated intervals by replacing inside functions with "u".

More Reimann Sums

Today in class, We learned how to find the left and right hand sums by using the area of the graph of a function. We also learned some rules for definite integrals and did some examples to use what we learned.

Riemann Sums

Today in class we learned how to do Riemann sums with infinite subintervals. When doing so, you should use the Right Hand Sum because it is simpler. Note: the limit as n approaches infinity of the Riemann sum with infinite subintervals is the same as the integral.

Antiderivatives

Today in math we discussed how to find antiderivatives in differential equations. We then took it a step forward and found the differential equation at a given point, and finally re-introduced Distance f(x), Velocity f'(x), and Acceleration f''(x).

Start of Ch. 4 (10-19-10)

Today we started ch. 4. We talked about antiderivitaves or anti-deferation. Mr. Vishack mentioned that we are going to go through this unit backwards in relation to how we went through deferential equations. He said that first we are going to learn the rules of antiderivitaves and then learn the concept from where the rules come from.