Derivative
Integrals
Limits
Formula
/Rules
/Rules
100
Differentiate:
3x^2
What is, 6x.
100
Solve:
int_1^6 12x^3-9x^2+2 dx
What is,
(3(6)^4-3(6)^3+2(6))-(3(1)^4-3(1)^3+2(1))
3250
100
When does a limit exist?
When the limit from the left is equal to the limit from the right.
100
What formulua is this?
d/dx (x^n)= nx^(x-1)
What is, the Power Rule
200
Solve for the derivative:
f(x)=(6x^2)/(2-x)
What is,
f'(x)=(24x-6x^2)/(2-x)^2
200
What is the name of an integral without limits of integration?
What is, an Indefinite Integral.
200
Solve:
lim_(x->2) (2x^2-x-3)/(x+1)
What is, 1
200
What formula is this?
(fg)'=f'g+fg'
What is, the Product Rule
300
What derivative is acceleration?
What is, the second derivative.
300
Solve:
int (2x)/(x^2+1) dx
What is,
ln abs (x^2+1)
300
What are 4 discontinuities learned in AP Calculus?
1. Cusp/Corner
2. Removable/Non-Removable
3. Vertical Tangent
300
When is this formula used?
d/dx(f(g(x)))= f'(g(x))g'(x)
What is, when differentiating a composite function.
400
What does f'(x) equal, if f(x)=
(6x^2+7x)^4
What is, f'(x)=
4(6x^2+7x)^3*(12x+7)
400
What does an integral find?
What is, the area from a curve to the X-axis.
400
Solve the limit:
lim_(x->4) (8-3x+12x^2)
What is, 188.
400
State/write the Quotient Rule
(f/g)^'=(f'g-fg')/g^2
500
Implicitly differentiate the following:
x^3+y^3=6xy
What is,
dy/dx=(6y-3x^2)/(3y^2-6x)
500
Solve:
int secx tanx dx
What is,
sec x+C
500
According to the graph:
A) Does the limit at f(-4) exist?
B) Does the limit at f(-1) exist?
C) Does the limit at f(2) exist?
D) Does the limit at f(4) exist?
What is,
A) The limit does not exist.
B) The limit does exist.
C) The limit does not exist.
D) The limit does exist.
500
What rule is this?
int_a ^b f(x)dx= F(b)-F(a)
What is, The First Fundamental Theorem of Calculus