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Level 551

Calculus AB : Useful Formulas


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limit of (sin(x)/x) as x approaches 0
0
limit of (1-cos(x)/x) as x approaches 0
cos(x)
Derivative of sin(x)
-sin(x)
Derivative of cos(x)
Sec^2(x)
Derivative of tan(x)
-csc(x)cot(x)
Derivative of csc(x)
sec(x)tan(x)
Derivative of sec(x)
-csc^2(x)
Derivative of cot(x)
V= (1/3)pi(r^2)h
Volume of Cone
V= (4/3)pi(r^3)
Volume of Sphere
V= x^3
Volume of Cube
V= 2pi(r^2)h
Volume of a Cylinder
0
Derivative of (u) (Note: I set u as a constant)
(e^u)(u')
Derivative of e^u
u'/u
Derivative of ln(u)
n(x^n-1)
Derivative of x^n
(1/u(lna))(du/dx)
Derivative of (log(a)u)
s(t)=1/2(g(t^2))+(vt)+s
Position Function
u'(lna)a^u
Derivative of a^u
sin(2x)
2sin(x)cos(x)
cos(2x)
2cos^2(x)-1
sin^2(x)+cos^2(x)
1
1+tan^2(x)
sec^2(x)
1+cot^2(x)
csc^2(x)
-cos(x)+C
Integral (sin(x)dx)
sin(x)+c
Integral (cos(x)dx)
-cot(x)+C
Integral (csc^2(x)dx)
tan(x)+C
Integral (sec^(x)dx)
sec(x)+C
Integral (sec(x)tan(x))
ln(x)+c
Integral (1/x)
e^u + c
∫ e^u du
ln(sec(x))
Integral (tan(x)dx)
ln(sin(x))
Integral (cot(x)dx)
ln(tan(x)+sec(x))
Integral (sec(x)dx)
-ln(csc(x)+cot(x))
Integral (csc(x)dx)
ln[u]+c
Integral (u'/u)du
1/sqrt(1-x^2)
Derivative of arcsin(x)
-1/sqrt(1-x^2)
Derivative of arccos(x)
1/(1+x^2)
Derivative of arctan(x)
(x^(n+1))/(n+1)
Integral (x^n)
Log(base b)(a^x)
x(log(base b)(a))
Log(a*b)
Log(a)+Log(b)
Log(a/b)
Log(a)-Log(b)
1
Log(base b)(b)
1
Log(base e)(e)
Ln(e^x)
x
(x^m)(x^n)
x^(m+n)
(x^m)/(x^n)
x^(m-n)
(x^m)^n
x^(m*n)
Integral (a to b) f(x)dx
Integral (a to c) f(x)dx + Integral (c to b) f(x)dx
((g(x)f'(x))-(f(x)g'(x))/((g(x))^2)
Derivative f(x)/g(x)
g(x)f'(x)+f(x)g'(x)
Derivative f(x)g(x)
cn
Sigma (1 to n) (c)
(n(n+1))/2
Sigma (1 to n) (i)
(n(n+1)(2n+1))/6
Sigma (1 to n) (i^2)
(n^3(n+1)^2)/4
Sigma (1 to n) (i^3)
0
Integral (0dx)
kx
Integral (kdx) (Note: k is a constant)
(a+b)^2
a^2+2ab+b^2
(a^2-b^2)
(a-b)(a+b)
(a+b)^3
(a^3+3(a^2)(b)+3a(b^2)+b^3)
(a^3+b^3)
(a+b)(a^2-ab+b^2)
Average Value
(1/b-a)(Integral (a to b) (f(x)dx))
Trapezoidal Rule
use trapezoids to evaluate integrals (estimate area)
x(ln(x))-x+c
Integral (a to b) ln(x)
0
Derivative of constant c
u'/(u(lna))
Derivative of (log(a)u)
a^u
a^u lna x u'