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Tuesday, January 13, 2009

More Accumulation Functions

Today's class we revisited the nDerive program in our calculators. The program calculates the derivative of a function and graphs it. We also went through all the parameters but went in depth with the parameter h. The default value of h in our calculators is .01. It uses that value to calculate .01 units to the right and .01 units to the left. The bigger the h value becomes the less accurate it will be. However, by adding too many zeroes to the right of the decimal makes the calculator think the number is just plainly 0(thank you joseph for pushing your calculator to its limits).



We were also shown a new program in our calculators called fnInt (math 9 on calculator). This is able to graph an accumulation function. The slide above shows the parameters of the program. The default h value for this is .001 if I heard correctly. One thing we were told was to never write fnInt on a test EVEER. I'm surprised I've never done something like that on a test.



Then we found out there was more than 1 fundamental theorem of calculus. The 2nd fundamental theorem of calculus is displayed above. All it says is that the derivative of an accumulation function is equal to the original function f(x). An accumulation function is a function made from using the area under the curve. Like the previous example before using fnInt, we saw that the graph it created was the antiderivative of the function x. So the derivative of the accumulation function would be the original function...(in terms of the example the original function would be x) That shows a connection between derivatives and integrals. They are like multiplying and division or adding and subtracting. Differentiation and integration are inverses of each other.

In between the learning there was chit chat about scholarships, Mr. K's new house, and other things I unfortunately didn't write down =(. Anywho next scribe will be Paul or Not_Paul...whatever name you go by XD.

1 comment:

Dr. Eviatar said...

Joyce, I really liked this:

"That shows a connection between derivatives and integrals. They are like multiplying and division or adding and subtracting. Differentiation and integration are inverses of each other."

I always think that these analogies show some deeper connection between numbers - back to its being all about relationships.

What do you think?

Cheers, Dr. Eviatar.