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BC Calc - Unit 7
| Question | Answer |
|---|---|
| ∫udv=... | uv - ∫vdu |
| Tabular Method | create a table; get u to zero OR something where across can be integrated/repeats the integrand |
| ∫🙂/(x-a)(x-b)=... | ∫A/(x-a)dx + ∫B/(x-b)dx |
| PFD: If The Degree Of The Numerator Is Greater Than Or Equal To The Denominator... | the first step is long division |
| When To Use Partial Fraction Decomposition | for quotients where denominator factors into linear |
| Improper Integrals (Limits To Infinity) | plug in "t" for ∞; set a limit outside where t->∞; use fundamental theorem of calculus; take the limit |
| II: If The Limit As "x" Approaches "∞" Gives You An Indeterminant... | use L'Hospital {f(x)/g(x)} |
| Improper Integrals (Discontinuity At Value) | girl...idek |
| Converges Versus Diverges | if the limit exists, it converges to a # ;; if the limit doesn't exist, it diverges |
| Euler's Method | x | y | dy/dx | dy/dx(h) |
| EM: How To Determine Step Size (h) | (final x value - initial x value) / number of steps |
| EGD: Given The Differential Equation "y'=ky" or "dy/dt=ky"... | then the solution is y=Ce^kt (rate of change is directly proportional to y) |
| EGD: What "k" And "C" Mean | k is the constant of proportionality ;; C is a constant |
| LE: Given The Differential Equation "y'=ky(1-(y/L))"... | the solution is y=L/(1+Ce^-kt) |
| LE: What "k" And "L" Mean | k is the constant of proportionality ;; L is the carrying capacity |
| LE: As x Approaches ∞... | y approaches L |
| LE: The Rate Increases The Fastest At... | y=L/2 |
Created by:
abievans
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