Equations Flashcards
e^0
1
ln(e)
1
ln(1)
0
e^infinity
infinity
e^negative infinity
0
ln infinity
infinity
e^lnx
x
logx(x)^a
a
a^loga(y)
y
ln(e)^w
w
definition of the derivative
(f(x+h)-f(x))/h
second definition of the derivative
(f(x)-f(a))/x-a
chain rule derivative of f(g(X))
(f’(x)g(x))(g’(x))
f(x)=a^x, f’(x)=?
(a^x)((ln)a)
sinx domain and range
(-pi/2,pi/2), (-1,1)
arcsinx domain and range
(-1,1), (-pi/2,pi/2)
cosx domain and range
(0, pi), (-1,1)
arccos x domain and range
(-1,1), (0,pi)
tanx domain and range
(-pi/2,pi/2), (-inf,inf)
arctanx domain and range
(-inf,inf), (-pi/2,pi/2)
lim (sinx/x)=
1
lim (1-cosx/x)=
0
sin(x+y)
sinxcosy + cosxsiny
sin(x-y)
sinxcosy - cosxsiny
1,2,rt3
pi/3,pi/6,90
1, rt2, 1
pi/4,pi/4,90
cos(x+y)
cosxcosy - sinxsiny
cos(x-y)
cosxcosy + sinxsiny
tan(x+y)
(tanx+tany)/(1-tanxtany)
tan(x-y)
(tanx-tany)/(1+tanx+tany)
sin2x
2sinxcosx
cos2x
1-2sin^2
tan2x
(2tanx)/(1-tan^2x)
sin^2x
(1-cos2x)/2
cos^2x
(1+cos2x)/2
