The third week of calculus didn’t seem as bad as the second week. Probably because it was just a review for the test on the first two days and the test was on Wednesday. We had a lot of intro to Calc on the test along with the stuff we learned in the first two weeks of Calculus. Some things on the test were points of discontinuity, like removables, jumps, infinites, finites, and vertical and horizontal asymptotes. Also, there was finding derivatives, product and quotient rule, arc trig functions, derivative of sin and cos, and other things that we learned in the first week or two of Calculus.
One thing I understood very well was how to find horizontal asymptotes. To find horizontal asymptotes, you must remember three rules.
1. If the degree on top is larger than degree on bottom, it’s infinity.
2. If the degree on top is equal to the degree on bottom, divide the coefficients.
3. If the degree on top is smaller than degree on bottom, it’s 0.
So if we were given (x^3 – 2x^4 + x + 3x^2 – 4) / (x^6), then the degree on top is smaller than degree on bottom, so the limit would be equal to 0.
Now, from what I heard, the stuff everyone learned on Thursday and Friday when I was absent was pretty difficult. I heard it was something about concavity, and I’ve never heard of that before. If anyone understands it and wants to give me a brief explanation it would be greatly appreciated :)
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thankfully, concavity is probably the easiest thing from the whole week =)
ReplyDeletewhen something is concave, it has a "dip"
..like a porabala would be concave.
now as far as up/down, b-rob explained it as:
concave up is like a bowl, allowing water in.
and concave down is like an ubrella, keeping
water out.
that's about as simple as it getss =)
Be sure to remember that Concave up comes from a postitive slope, and concave down from a negative slope. The concavity can also tell you if the derivative starts below or above the axis
ReplyDeleteConcavity is when a graph curves up or down. It'll be in either a parabola or an x^3, or so on term. When there is a positive slope to the graph, the derivative will concave up (it will have a bowl shape, where you can pour stuff into it). If the graph has a negative slope, the derivative will concave down, giving it an umbrella shape.
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