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Doublecheck if you're unsure!
We need to memorize basic integration formulas, such as the integral of tangent, or sec. Although it's not that difficult, I realized if you're not sure you can always re-check what you did by deriving. Ex. integral of tanx = ln|secx| and the derivative of ln|secx|=(secxtanx)/secx = tanx. Correct! -
Period: to
Spencer Calc
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Growth/Decay
When a problem states: Bacteria have a half-life of y years and starts with p population ..this means you use the two points in terms of (time, population): (0,p) and (y,p/2) -
Slope Fields
When determining if a slop field is a certain function or vice versa look first if the slops of 0 (horizontal line) and undefined (vertical) match! -
Inverse Function
The derivative of the inverse function is very easily defined using the chain rule and the fact that f(g(x))=x, assuming g(x) is the inverse of f(x).
d/dx[f(g(x))=x]
f '(g(x))g'(x)=1
g'(x)=1/f '(g(x)) -
Conics
The equations of a circle and of an ellipse are really the same. A circle is a special type of ellipse in which a=b and the major/minor axises are the same length! -
Indeterminate Forms
It never made sense to me how 1^infinity didn't equal one, but now I understand that that DOES =1. However, when we're talking about LIMITS, a number APPROACHING one does not equal one, such as the lim (.01)^infin -
Geometric/P-Series
If you just think about how series work, then there's less memorization. In geometric series |r| must be less than one otherwise the terms would keep getting bigger and bigger ininitely approaching not one particular number. Similarly with p-series. With a p<1, the denominator keeps getting smaller and thus the whole fraction gets larger. This also means the terms will keep getting bigger and bigger and will diverge. -
RatioTest
The Ratio test makes sense because is the ratio between the next term over the previous term is less than one that means all the terms are getting smaller and thus converges! -
Sinx and Cosx
The taylor expansion of sinx about 0 is very similar to the expansion of cosx about pi/2! As is cosx about 0 very similar to sinx about pi/2! This is becase sin(0)=cos(pi/2) and sin(pi/2)=cos(0) -
d/dx(sinx &cosx)
Take the derivative of the taylor expansion of sinx....it looks like taylor expansion cosx!! Also, the taylor expansion of cos x, looks like -sinx! These formula's we've memorized make sense! -
Computer Science
Having the computer science ap the day before the big game was stressful, but it got me into the right mindset. It got that side of the brain warmed up!
