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Mean Value Theorem
I completely forgot about the mean value theorem for integrals. All it says, essentially, is that there is some point where the average value of a function is equal to f(c). -
Period: to
April 11-Calc AP
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Logistics Growth
I have to remember both formulas for the logistic equations, the differential equation, and the actual solution. In the actual solution, I had forgotten that A (or sometimes P, depending what book is being used) is the carrying capacity. The denominator of the solution shouldn't be so hard to remember since 1+ce^(-Akt) is similar to the ce^kt equations we used to do. -
Inverse Trig
I completely forgot the derivative/integration formulas for inverse trig. Fortunately, after looking through them again, they're easy to memorize since they all have basic patterns. For instance, the derivative of arctanu is 1/(1+u^2) and the derivative of arccotu is simply the negative form. -
Integrals with Infinity
After review, I remembered that although integrals with infinity look weird, they're pretty easy. Just take the limit as c approaches infinity of the integral (with c replacing the infinity sign). When you solve the integral, there should be a nice outcome, with some things cancelling out (like the limit as c approaches infinity of 1/c is 0). -
Tabular Method for Integrals
When doing integrals resembling things like int(x^2 * e^x), I don't have to do parts twice. Instead I can make a chart of alternating signs (starting with plus), u (which will differentiate to 0), and dv (which I will integrate). The first sign, the first u term, and the second dv term go together, and the pattern continues. This should save lots of time on the ap. -
Ratio Test for Series
When finding the interval of convergence of a series, Use the ratio test. I must remeber to check the endpoints! this is done by plugging them into the series and seeing if it converges or diverges. I also must remember that if the limit is infinity, then R=0 and if the limit is 0, R=infinity (since the limit must be less than 1 for convergence) -
Taylor Series
Even if I forget the power series for some of the important functions (like e^x, sinx, cosx...) I must remember the form of the general taylor series. If centered about c, it's f(c) + f'(c)(x-c) + f''(c)(x-c)^2/(2) + f'''(c)(x-c)^3/(3!)... Even if I forget what sinx is in power series form, I can always write out a taylor series quickly, and find the general term. -
Disc/Shell Method
I must remember that the disc method should be used when my rectangle is perpendicular to the axis of revolution and the shell method should be used when my rectangle is parallel to the axis of revolution. The disc method is the one using pi, R^2, and r^2. Shell is the one that uses 2pi, p(x), and h(x). -
Endpoints
I'm constantly forgetting to check the endpoints when finding maximums and minimums. After finding critical values when the derivative equals 0, i have to remember to plug the endpoints into the equation. especially for the free response questions -
Parametrics
there's essentially very little to memorize in terms of parametrics. the distance formula is very self explanatory (since it's just the integral of the magnitude of velocity, which is speed). taking the integral of the speed, which is in distance/time, will just give you distance. finding dy/dx is also self explanatory since (dy/dt)/(dx/dt) cancels out the dts to give you dy/dx. -
Glad that's over
That was, honestly speaking, one of the easiest tests i've taken. I was surprised as to how much of it wasn't bc and how much of it was strictly ab. There was only one multiple choice question that I was unsure of, which was the derivative of the inverse of a function. aside from that, I'm extremely confident on the multiple choice. The free response was also good. I breezed through the parametrics question and the tea cooling question. The one that was iffy was number 6, the taylor question
