Dihrivities
Integrals
Trihgonometry
Limits
Calc Rules/Formulas
100
Derivative of c
0
100
The integral of sin(x)
cos(x)
100
The derivative of sin(x)
-cos(x)
100
Condition for limit to exist at x = c
left & right hand limits both exist AND are equal to each other
100
(fg)' = (f')(g) + (f)(g)'
What is the Product Rule?
200
Derivative of ln(x^2)
2/x
200
The integral of x dx
((x^2)/2) + C
200
Derivative of
cos(4x^2 + 2x)
-sin(4x^2 + 2x)(8x + 2)
200
Evaluate the limit as x approaches 4 for
(x^2 - 16)/(x - 4)
8
200
Used as a work around when finding the limit of (f(x)/g(x)) naturally leads to either (0/0) or (∞/∞)
What is L'HOSPITAL's Rule?
300
Derivative of
4x^4 - 3x^2 + 7x - 16
16x^3 - 6x + 7
300
∫1/(x2+1) dx
arctanx+ C
300
(Radical 3) / 2
What is cos(30°)
OR
What is sin(60°)
300
Evaluate the limit as x approaches ∞ for
(3x^2 - 5x)/(2x^2 + 7)
3/2
300
This theorem can only be used if a function is continuous on [a,b], differentiable on (a,b), and f(a)=f(b).
What is Rolle's Theorem?
400
derivative of f(g(x))
f'(g(x)) g'(x)
400
∫(3x2+4x−5)dx
x3+2x2−5x+C
400
derivative of
f(x) = arccos(3x)
-3 / (radical (1-9x^2))
400
What derivative is represented by the limit as h approaches 0 for
(tan(x+h) - tan(x)) / h
sec(x)^2
400
What is Midpoint Riemann Sum?
500
Derivative of x^x
(x^x)lnx+1
500
∫(2x+3)/(x2+3x+2) dx
ln(x2+3x+2)+C
500
derivative of
f(x) = tan(x)^3
3tan(x)^2 sec(x)^2
500
What is the limit as h approaches 0 for
(ln(e^2 + h) - 2)/h
1/e^2
500
A mathematical method that helps you determine the possible number of positive & negative real roots (zeros) of a polynomial function
What is Descartes' Rule of Signs?