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tan x =
sin x/cos x
cot x =
cos x/sin x
sec x =
1/cos x
csc x =
1/sin x
double angle id’s
2sinxcosx = sin2x, cos2x - sin2x = cos2x
Pythagorean id’s
sin2x+cos2x=1, sec2x-tan2x = 1
Even - odd id’s
sin(-x) = -sinx, cos(-x) = cosx, tan(-x) = -tanx
sin(A+B) =
sinAcosB + cosAsinB
cos(A+B) =
cosAcosB-sinAsinB
sin(A-B) =
sinAcosB-cosAsinB
cos(A-B) =
cosAcosB+sinAsinB
|x| =
x if x>=0, -x if x<0
Law of cosines
c² = a²+ b² - 2abcosC
Distance between two points
sqrt[(x2-x1)2+(y2-y1)2]
midpoint formula
( [x1+x2]/2 , [y1+y2]/2 )
ln(ab) =
lna + lnb
ln(a/b) =
lna - lnb
ln(an) =
nlna
ln(1/a) =
-lna
ln(0) =
undefined
ln(1) =
0
ln(e) =
1
One sided limit, from the left
limx→a-f(x)=L
One sided limit, from the right
limx→a+f(x)=L
Definition of a limit
limx→af(x)= L iff limx→a-f(x)=L=limx→a+f(x)
sin =
y
cos =
x
lim (f+-g) =
limf +- limg
lim(c x f) =
c x limf
lim(fg) =
limf x limg
lim(f/g)
limf/limg for lim≠0
limx→ak =
k
limx→ax =
a
limx→asqrt(f(x)) =
sqrt(limx→af(x))
limx→af(g(x)) =
f(limx→ag(x)) provided that f is continuous at lim x >=a of g(x)
definition of continuity
A function f is continuous at x=c iff
f( c) exists
limx→cf(x) exists
limx→cf(x)=f(c )
Intermediate Value Theorem
if
f is continuous on the closed interval [a,b]
f(a) ≠f(b)
k is between f(a) and f(b)
then there exists a number c between a and b for which f(c ) = k
Squeeze theorem
if f(x)<=g(x)<=h(x) and limx→af(x) = limx→ah(x) then limx→ag(x) =L
common limits, limx→0
limx→0sinx/x = 1,limx→01-cosx/x = 0
Common limits, limx→a
limx→ax = a
Common limits, limx→0-
limx→0-1/x → -infinity
Common limits, limx→0+
limx→0+1/x→ infinity
Note 
Flashcard (20)