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Level 599

BC Calculus: Formulas


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1
sin^2 x+cos^2 x=
1+cot^2 x=
csc^2 x
tan^2 x+1=
sec^2 x
1/2(1-cos2x)
sin^2 x=
1/2(1+cos2x)
cos^2 x=
x=(-b±√(b^2-4ac))/2a
Quadratic Formula
A=√3/4 s^2
Area of an Equilateral Triangle
A=1/2(b1+b2)h
Area of a Trapezoid
A=1/2bh
Area of Triangle
A=πr²
Area formula with radius
Slope of a Line
m = (y2 - y1) / (x2 - x1)
y-y₁=m(x-x₁)
Point-Slope form
ln(1)=
0
e^lnx=
x
|x|=
{(x, x≥0
Odd Function
sin x, odd or even?
Even Function
cos x, odd or even?
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
1
lim (as x approaches 0) sinx/x=
0
lim (as x approaches 0) (1-cosx)/x=
Limit Definition of Derivative (1)
lim(as h approaches 0) [f(x+h)-f(x)]/h
Limit Definition of Derivative (2)
lim (as h approaches 0) [f(a+h) - f(a)]/h
Limit Definition of Derivative (3)
lim (as x approaches a) [f(x)-f(a)]/[x-a]
0
lim (as x approaches infinity) sinx/x=
e
lim (as n approaches infinity) [1+(1/n)]^n=
cu'
d/dx [cu]=
u'±v'
d/dx [u±v]=
uv'+vu'
d/dx [uv]=
[vu'-uv']/v^2
d/dx [u/v]=
0
d/dx [c]=
d/dx [u^n]=
nu^(n-1) u'
1
d/dx [x]=
u'/u
Derivative of ln(u)
u'e^u
d/dx [e^u]=
d/dx [log_a(u)]=
u'/(ln a)u
d/dx [a^u]=
u'(ln a)a^u
(cos u)u'
d/dx [sin u]=
-(sin u)u'
d/dx [cos u]=
(sec^2 u)u'
d/dx [tan u]=
-(csc^2 u)u'
d/dx [cot u]=
d/dx [sec u]=
(sec u tan u)u'
d/dx [csc u]=
-(csc u cot u)u'
1/[f'(f^-1(x))] or 1/[f'(inverse f(x)]
(f^-1(x))' or d/dx [Inverse f(x)]=
u'/√(1-u^2 )
d/dx [arcsin u]=
-u'/√(1-u^2 )
d/dx [arccos u]=
u'/(1+ u^2)
d/dx [arctan u]=
-u'/(1+ u^2)
d/dx [arccot u]=
d/dx [arcsec u]=
u'/[ |u| √(u^2-1) ]
d/dx [arccsc u]=
-u'/[ |u| √(u^2-1) ]