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Calc II and Review
things
58
Mathematics
Undergraduate 1
01/27/2015
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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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