We have been learning about limits, and now it seems that we are wrapping them up. While limit themselves seem to have little application, they led us into the next unit which is derivatives. This is something totally new. I remember doing the equation with the f(x+h) and all that junk last year and I didn't understand any of it. In order to better understand derivatives, we were given an activity to explore how they work. Using desmos.com, we were supposed to recreate the graph that Mr. Cresswell had, and create the same type of lines and points. The graph was .5x^2 with a fixed point, a sliding point on the curve, and a line connecting the two points. With two points on the function connected by the line, the line was always inside of the curve, creating a secant line. We were supposed to see what happens as the sliding point became closer and closer to the fixed point. It turns out that as the sliding point becomes closer and closer to the fixed point, the line wants to touch at just one point on the curve, creating a tangent line. I believe that this is what a derivative is, the slope of the tangent line through a point. It is much like a limit how the sliding point gets closer and closer and closer to the fixed point, but it can never be the same point because then it wouldn't be a specific line anymore. I think that this is interesting.
https://drive.google.com/file/d/0B9SIejrlItGYYVRIZUYySVg1OEU/edit?usp=sharing
The second graph consisted of the same function, but now with both points moving instead of just one. When close together, it roughly represents how the tangent line slides along the function.
https://drive.google.com/file/d/0B9SIejrlItGYbE5uUFU1Vjc5ZlU/edit?usp=sharing
The third graph was intended for us to explore different types of graphs and the tangents of them. I had a bit of fun with this, doing all kinds of tans and cos' and sins with square roots and exponents and things, creating all kinds of cool graphs. I did it 4 days ago, so I don't really remember exactly what the equation was for the one we chose to do.
https://drive.google.com/file/d/0B9SIejrlItGYQVhKMldpWExfNkk/edit?usp=sharing
I think i might be missing something because I see no relation to how the worksheet we got in the beginning of class related to the activity we did. In general however, the activity helped me understand derivatives and if nothing else, introduced me to a new math site that could be helpful.
https://drive.google.com/file/d/0B9SIejrlItGYYVRIZUYySVg1OEU/edit?usp=sharing
The second graph consisted of the same function, but now with both points moving instead of just one. When close together, it roughly represents how the tangent line slides along the function.
https://drive.google.com/file/d/0B9SIejrlItGYbE5uUFU1Vjc5ZlU/edit?usp=sharing
The third graph was intended for us to explore different types of graphs and the tangents of them. I had a bit of fun with this, doing all kinds of tans and cos' and sins with square roots and exponents and things, creating all kinds of cool graphs. I did it 4 days ago, so I don't really remember exactly what the equation was for the one we chose to do.
https://drive.google.com/file/d/0B9SIejrlItGYQVhKMldpWExfNkk/edit?usp=sharing
I think i might be missing something because I see no relation to how the worksheet we got in the beginning of class related to the activity we did. In general however, the activity helped me understand derivatives and if nothing else, introduced me to a new math site that could be helpful.