Limits/Continuity
Derivatives
Integrals
Polar/Parametric
Series
100
lim_(x->2) (x+1)/(x-2)
What is limit doesn't exist? (and you must say it like Lindsay Lohan in Mean Girls.)
100
d/dx (ln x)
1/x
100
int e^x dx
What is
e^x + C
100
Who is Vector
100
sum_(n=0)^oo (6/7)^n
What is 7?
200
lim_(h->0) (f(x+h)-f(x))/h
What is the limit definition of derivative?
200
d/dx (sin(3x^2+4))
6x cos(3x^2+4)
200
The approximation to the area under a curve by chopping up the interval into infinitely many tiny sections.
What is a Riemann Sum?
200
The formula
int sqrt((dx/dt)^2 + (dy/dt)^2) dt
What is the speed formula?
200
The type of series where
lim_(n->oo) a_n !=0
What is diverging series?
300
If a function is differentiable, then it must be ??
what is continuous?
300
lim_(x->a) f(x)/g(x) = lim_(x->a) (f'(x))/(g'(x))
What is the L'Hopital's Rule?
300
int 1/(4x+5) dx
What is
1/4 ln |4x+5| + C
300
This is the formula to convert polar coordinates
(r,theta)
to rectangular coordinates (x,y) for the x-value.
What is
x=r cos theta
300
The function whose Taylor Series expansion is
f(x)=x-x^3/(3!)+x^5/(5!)-...
What is sin x?
400
If the function f is continuous, then there is a point c, a<c<b, such that f(a)<f(c)<f(b).
What is the intermediate value theorem?
400
dy/dx(xy)=xy'+yx'
What is the product rule?
400
This formula
int u dv= uv - int v du
What is integration by parts (the reverse of product rule)?
400
The general formula for finding the area of a polar curve.
What is
1/2 int [r(theta)]^2 d theta
400
The type of error bound states that the approximation must be within the absolute value of the next omitted term.
What is the alternating series error bound?
500
If the function f is continuous and differentiable, then there is a point c, a<c<b, such that
(f(b)-f(a))/(b-a)=f'(c)
.
What is the mean value theorem?
500
This type of curve is an exponential curve with a upper limit.
What is a logistic curve?
500
The theorem that says if f is an integrable function with F as its antiderivative, then
int_a^b f(x) dx = F(b) - F(a)
What is the Fundamental Theorem of Calculus (part 2)?
500
The slope of the tangent line for a polar function
r=f(theta)
What is
dy/dx= (r' sin theta +r cos theta)/(r' cos theta - r sin theta)
500
These are the only two types of series that you can find the actual sum of the series.
What are geometric and telescoping?