Limits and Continuity
Differentiation
Theorems
Integration
Differential Equations
100
Is this graph continuous?
Yes
100
lim_(h->0)(f(x+h)-f(x))/h
What is the limit definition of a derivative
100
For some interval [a,b] on a continuous f(x), there must exist some local maximum and minimum
Extreme Value Theorm (EVT)
100
What is f(x) if f'(x)
= x^n
(x^(n+1))/(n+1) + C
100
what is d/dx of
x^2y - xy^2
2xy(dy/dx)-2y(dy/dx)
200
What is
lim_(x->1/3)(2x-1)^2/x
1/3
200
what is f'(x) if f(x) =
x^n
f'(x) = nx^(n-1)
200
For some interval [a,b] on a continuous f(x) some value c must exist that
f(a) <= f(c) <= f(b)
What is the Intermediate Value Theorem
200
What is
int_0^1x^3dx
1/4
200
what is y if
dy/dx = x^4/(2y)
y = sqrt((x^5)/5)
300
What is
lim_(x->4)f(x)
8
300
When is the ball at its peak if the height is modelled by
h(t) = -5t^2+12.5t
t = 1.25
300
For some interval [a,b] on a differentiable f(x),
f'(x) = (f(b)-f(a))/(b-a)
What is the Mean Value Theorem
300
Riemann Sum
What is an approximation of an Integral
300
What is the equation of this slope field
x^2 + y^2 = 1
400
What is the limit of
lim_(x->2)(x^3-8)/(x-2)
12
400
What rule states
f(x) = g(h(x)) f'(x) = h'(x)g'(h(x))
The Chain Rule
400
d/dxint_a^xf(t)dt = f(x)
What is the First Fundamental Theorem of Calculus
400
what is f(x) if
f'(x) = cos(x)
-sin(x) + C
400
What is the general solution for
5dy/dx + x = 0
y = -x^2/10 + C
500
What is
lim_(x->oo)(7x^2-5x+53)/(3x^2+1999x-pi)
7/3
500
What is f'(x), f(x) =
e^x
e^x
500
int_a^bf'(x)dx = f(b)-f(a)
What is the Second Fundamental Theorem of Calculus
500
what is f(x) if f'(x) =
e^x
e^x+C
500
if dr/dt = 5 what is the change of a cylinder when the radius is 3 and height is 1
30pi or 94.25