# Shared Flashcard Set

## Details

Calc II and Review
things
58
Mathematics
01/27/2015

Term
 ln(e)=
Definition
 1
Term
 function of sin(x)
Definition
 f(x)=a*sin(b(x+c))+d; a=amplitude, b=period, c=phaseshift left, d=midline
Term
 sin 2x =
Definition
 2 sin x cos x
Term
 cos 2x =
Definition
 cos^2 x - sin^2 x = 2 cos^2 x - 1 = 1 - 2 sin^2 x
Term
 tan x =
Definition
 sin x / cos x
Term
 1 + tan^2 x =
Definition
 sec^2 x
Term
 1 + cot^2 x =
Definition
 csc^2 x
Term
 d/dx (sin x) =
Definition
 cos x
Term
 d/dx (cos x) =
Definition
 -sin x
Term
 d/dx (tan x) =
Definition
 sec^2 x
Term
 d/dx (csc x) =
Definition
 -csc x cot x
Term
 d/dx (sec x) =
Definition
 sec x tan x
Term
 d/dx (cot x) =
Definition
 -csc^2 x
Term
 integral u dv =
Definition
 uv - integral v du
Term
 sin^2 x + cos^2 x =
Definition
 1
Term
 upside-down A
Definition
 for all
Term
 backwards E
Definition
 there exists
Term
 funky 3
Definition
 such that
Term
 backwards funky 3
Definition
 ...is an element of...
Term
 F =
Definition
 ma, m(d^2s)/(dt^2)
Term
 newton =
Definition
 kilogram-meters/second^2
Term
 W =
Definition
 Fd (only when F is constant), metric units are newton-meters aka Joules, US units are foot-pounds
Term
 product rule
Definition
 d/dx (f(x)g(x)) = f'(x)g(x) + f(x)g'(x)
Term
 quotient rule
Definition
 d/dx (f(x)/g(x)) = [f'(x)g(x) - f(x)g'(x)]/[g(x)]^2
Term
 chain rule
Definition
 d/dx f(g(x)) = f'(g(x))*g'(x)
Term
 integral 1/(a^2 + x^2) dx =
Definition
 integral 1/(a^2 + x^2) dx = (1/a)tan^-1(x/a) + c
Term
 d/dx cos^-1(x) =
Definition
 d/dx cos^-1(x) = -1/(sqrt(1-x^2))
Term
 Antiderivative of a sum
Definition
 is the sum of the antiderivatives
Term
 integral a^x dx
Definition
 (a^x)/lna + c
Term
 sec^2x =
Definition
 sec^2x = 1+tan^2x
Term
 csc^2x =
Definition
 csc^2x = 1 + cot^2x
Term
 integral ln(x) dx
Definition
 x(log(x)-1) + c
Term
 integral sinx dx
Definition
 -cosx + c
Term
 integral cosx dx
Definition
 sinx + c
Term
 integral tanx dx
Definition
 ln|secx| + c = -ln|cosx| + c
Term
 d/dx logax =
Definition
 1/(xlna)
Term
 d/dx a^x
Definition
 a^x(lna)
Term
 y = loga(x) <=>
Definition
 a^y = x
Term
 Mean Value Theorem for Integrals
Definition
 If f is continuous on [a,b], then there is a number c in [a,b] where the function takes on it's average value such that f(c) = 1/(b-a) intergral [a,b] f(x) dx
Term
 aln(x) =
Definition
 ln(x^a)
Term
 integral du/u =
Definition
 ln|u| + c
Term
 favg =
Definition
 1/(b-a) intgral from a to b f(x) dx
Term
 e^(lna) =
Definition
 a
Term
 integral x^-1 dx =
Definition
 ln|x| + c
Term
 loga(x^r) =
Definition
 rloga(x)
Term
 loga(x1/x2) =
Definition
 loga(x1) - loga(x2)
Term
 loga(x1x2) =
Definition
 loga(x1) + loga(x2)
Term
 loga(x) in natural log form
Definition
 lnx/lna
Term
 y = lnx <=>
Definition
 e^y = x
Term
 Def of 1 to 1 function
Definition
 If it never takes on the same value twice. f(x1) =/ f(x2) whenever x1 =/ x2
Term
 formula for the derivative of an inverse
Definition
 (f^-1)'(x) = 1/(f'(f^-1(x)))
Term
 (f^-1)'(a) =
Definition
 1/(f'(b))
Term
 e (as a limit) =
Definition
 limit as n->inf., (1 + 1/n)^n = e
Term
 cot x =
Definition
 cos x / sin x
Term
 HAF: cos^2 x =
Definition
 (1 + cos 2x)/2
Term
 HAF: sin^2 x =
Definition
 (1 - cos 2x)/2
Term
 sec^2 x =
Definition
 1 + tan^2 x
Term
 d/dx sin(ax) =
Definition
 a*cos(ax)
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