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Fundamental theorem of Calculus
Somehow, in my studies of calculus, I forgot the fundamental theorem of calculus. (the name of such a theorem would suggest that it is a bit important in calc class...) anyway, Today I was reminded of the two parts to this theorem:
first: d/dx[integral of f(x)]= f(x) ("like dividing multiplication!") second: integral from a to b of f(x) is F(b)-F(a).... most of that is obvious when written out this way, and yet, I can't ever seem to remember...
integral from a to b of f(x)= F(b)-F(a) -
Period: to
AP Calc Review
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Euler's Method
Euler's method and I don't usually get along, but recently, I've been trying to make peace with Euler. I usually can't remember the process, so I'll write it out here:
1. make chart- n,x, y, [dy/dx], dy.ysub(n+1)
2. fill in n, x and y according to information give to you in problem
3. find dy/dx
4. multiply by dx (given in problem) to find dy
5. add dy to y to get ysub(n+1)
6. n=1, x=starting x value plus dx, y=previous ysub(n+1)....
and continue!
also, important to note- this is an estimate! -
Free Response Day 1
Molly and I worked on the first part of the free response for the practice AP.The second one tripped us up. and we spent too much time wondering if it was polar just because the line was diagonal and started at the origin. I am just now getting back into the swing of test taking, remembering how precious time is on those free response questions. -
Free Response Day 2
Today I worked with Ben, because Molly was absent. I had some trouble "justifying" my answers, because often I would look at the graph and know the answer, but have forgotten the theorems behind that answer. I got great practice at talking my way around the names of theorems today, as I forgot many names of things, but remembered the concepts. My answers were probably too wordy for a calc free response, but whatever! -
Series and Plane Trips
Today we reviewed Series, which I feel pretty confident on, only really needing review on the remainder (abs(s-sn)+ abs(Rn) is less than or equal to a)
More interestingly, today I flew to St.Louis for spring break, and on the plane met two other people who were taking calc classes. One was even another high school senior, though she said she was in AB. we breifly discussed the trickiest parts of finding volumes of revolution and the fact that we both usually forget the pi at the beginning! -
Review of complex integrals
Today we worked on some complex integrals. Most importantly, we reviewed using udv substitution. I remembered the formula (int(udv)=uv-int(vdu))
however, what I had forgotten was LIPET, or the heirarchy of what to use for u. (though the PET part is somewhat dependant on what is easiest)
so, note to self: ***LIPET: Logs, inverse trig, polynomials, exponentials, trig. ** -
Debrief of Practice AP
I got a 72! Which translates to a five!!!!!!!!!
...but only barely- so more review is ahead of me-
the problem that I got wrong that really shocked me was number 39, y=sin(lnx) where they asked you to count the zeros. I thought I was definitely right, looking at the graph. Now I know to solve algebraically too, to avoid window problems! -
Intervals of Convergence
This sounds terrible, but until today, I had completely forgotten about intervals of convergences. The ratio test came back to me pretty quickly, but it took me a minute to realize that when the limit equaled infinity, I hadn't made a mistake- the interval of convergence was just 0! (<That exclamation point is NOT a factorial....) This realization caused me to also remember that when the limit equaled zero, the interval of convergence would be infinite (or all real numbers)... good to know! -
Volumes of Revolution
I had forgotton the shell method, but luckily the formula looks a bit like a word to me "volume = integralof [2(pi)rhdx]" ... this method also reminds me of those russian dolls in my grandmother's house.... -
Format questions...
Today I took the psychology exam. Midway through the exam, I realized that there were only two essays, not three. To avoid such a shock on the calc test, I did a bit of research and learned that the calc test this year would have two calculator problems followed by four non calculator problems, which is significantly different from last year.. Glad I checked! -
Nature walk and comforting thoughts...
Today I realized that besides needing to look over a few integration formulas one last time, I'm really prepared for this test. Bring it on, AP! -
THE BIG GAME!!!
Cold armory, sixth derivatives, rain... blehhh. My head did hurt, but I feel like I did pretty well!
SUCCESS!
