So it’s 8:56 on Sunday night and I’m actually doing my blog on time. Look at that! ha. This week off was a nice break. I had a lot of time to do things, although I procrastinated until the very last minute. Good thing I was off today.
Anyway, two weeks ago right before B-rob left we had two days of review of the things that were bothering us the most. I blogged about this last week, but I saved some things to blog about this week as well. A few more things that refreshed my memory are how to do a derivative and integral in my calculator, definitions of derivatives, how to recognize product rules and chain rules, composite functions and composite functions with graphs, e integration, and ln integration.
Ok, so for using my calculator. For the calculator portion the calculator can be used for every problem to help, so I need to remember to graph in it as much as possible. For an integral in the calculator, I plug it into y=, although you can do it with the math function. The way I do it is I plug the integral into my y=, I graph it, hit second calc, and go all the way down to integral. Once I press that button, I just plug in my bounds and it gives me my integral. The way to do it with the math function is to hit math, fnint (equation, x, bound 1, bound 2). For this one, I always forget that x, or I don’t use enough parentheses.
Ok, so I’m still a little shakey when it comes to tables and composite functions. When there is a composite function, treat it as a chain rule and go from there. That was my biggest problem, I just did the composite without taking the derivative of it.
For integration with fractions, before substitution is considered, two things should be looked for: natural logs and tangent inverses. A natural log is when the top is the derivative of the bottom. A tangent inverse is when it is a number over x^(something) + 1.
I’m still not that great when it comes to particle problems.
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A specific example would be easier to explain, but for particle problems, they are usually asking for changes in direction. In that case, set velocity equal to zero and solve for x. Then set up intervals.
ReplyDeleteRemember its position, velocity, then acceleration.
The most recent particle problem we had is
A particle's position is given by s=t^3 - 6t^2 + 9t. What is its acceleration at time t=4?
Since you are given position and looking for acceleration, you have to take the second derivative.
s' = 3t^2 - 12t
s''= 6t - 12
Now just plug in 4.
6(4) - 12 = 12
for particle problems just remember pva!
ReplyDeleteit's position, velocity then acceleration.
meaning if you go down the list, take the derivative.
down-derivative
going up it, integrate!