Week+18+Jan+12-16

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Monday January 12, 2009
Today in class, we learned the definition of a definite integral. Ms. Gentry began with a simple equation which made it easier for the students to understand the basics. Using the limit of Riemann's sum as n approaches infinity, it was possible to find the definite integral for an interval. The definite integral was able to be confirmed by taking the antiderivate of the equation, substituting each end of the interval into the new equation, and subtracting the right side from the left. Below is a slide show of sample problems from Monday. media type="custom" key="2988624" Drew was reminded to use limit notation. Otherwise, this happens.

Tuesday January 13, 2008
Today we went over homework problems. We were given 3 different problems to do ranging from easy to hard. Below are the slides from today. media type="custom" key="2989342"

Wednesday January 14
The Mean Value Theorem states that if a function is continuous on a closed interval [a,b] and differentiable on the open interval (a, b) then there will be a point c, in the interval (a,b) where the slope of the tangent line to the function at c is equal to the slope of the secant line from x = a to x = b. The exploration exercise we did to introduce this theorem is shown in the slide-show below. media type="custom" key="2997510"

Thursday January 15th
The quiz required us to pick one of three definite integral problems to evaluate using a limit of a Riemann Sum. Following the quiz, we worked a couple of Mean Value Theorem problems, one of which is shown below.

If f(x) = x³ - x², find the value of c which satisfies the conclusion of the Mean Value Theorem on the interval [0,5].



Friday January 16th
Big day! The fundamental Theorem of Calculus. Today we worked through an exploration to derive the fundamental theorem of calculus.