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Today we went over integrals, from basic ones from Calc AB to more complex ones like ones involving partial fractions or 'u' and 'v' substitution. I need to review integreals with trig substitution. We also went over Riemann sums.
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We looked at differential equations and how to solve simple ones, but like Mr. Hyman said, there won't be any Bernoulli or first order differential equations. We went over logistics growth models and equations involving carrying capacity. One thing that I have to go over again is Euler's Method.
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We went over sequences and series, especially how to determine whether a series converges using the many different tests. This is definitely something I will need to go over again, specifically when to use each test and what each test determines/does not determine.
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Today we went over Taylor Polynomials, focusing mostly on which equations we should have memorized (sin, cos, e^x, lnx), but also how to find a Taylor Polynomial of the nth degree using derivatives. I need to remember to always use factorials in the denominator when finding Taylor Polynomials, as this is something I often forget to do.
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Today we went over advanced integration techniques like partial fractions and 'u' and 'v' subsitution. Trig subsitution integrals will not be on the AP exam. I need to review the integrals for inverse trig functions.
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Finding the volume of integrals using the shell and disc methods by revolving function around x or y axis. Also how to find area using cross sections with the base of a two-dimensional figure. I need to review the shell method and how to find R and r.
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Today we walked around the school and Mr. Hyman gave us his Hyman Helpflul Hints.
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