Derivatives
Integrals
Limits
Differential Equations
Hodge Podge
100
The slope of the tangent line to the graph
f(x)=3x^2-sinpix
at the point
x=2.
What is
12-pi?
100
An object has a velocity given by the equation
v(t)=4t+e^(t-2).
At t=2, the object's position, s(t), is given by s(2)=3.
This is the function that describes the object's position for any time t>0.
What is
s(t)=2t^2+e^(t-2)-6?
100
This is the solution of
lim_(x->5)((x^2+2x-35)/(x^2-25)).
what is
6/5?
100
Let
y'=1/3y
be the differential equation that models the population growth of rabbits. At time t=0, there are 50 rabbits. This is how many rabbits there are after 9 years.
What is
50e^3
rabbits?
100
This is a necessary and sufficient condition for a function f to be continuous at the point
x=4.
What is
lim_(x->4)f(x)=f(4)?
200
This is the derivative of
f(x)=(x^3sinx)/(x^2+3).
What is
f'(x)=(x^3cosx+3x^2sinx)/(x^2+3)-(2x^4sinx)/(x^2+3)^2?
200
This is the antiderivative of
f(x)=sinx+4x-e^-x.
What is
f(x)=-cosx+2x^2+e^-x?
200
This is the solution to
lim_(x->1)((2x^2+x-3)/(1-x^2)).
What is
-5/2?
200
This is the solution to the differential equation
dy/dx=x^2/y^3,
where y(3)=3.
What is
y=root(4)(4/3x^3+45)?
200
This is true about the continuity of a function f given above.
What is, f is continuous and differentiable everywhere except at the point where x=2?
300
This is the derivative of
x^2-xy+y^3=8.
What is
(y-2x)/(3y^2-x)?
300
This is the solution to
int_-1^2(3x^2-4x+2)dx.
What is 9?
300
This is the solution to
lim_(x->oo)((x^2-3x+7)/sqrt(4x^4-3x^3+2x^2)).
What is
1/2?
300
This is the differential equation for the following slope field. 
What is
dx/dy=x/(y-1)?
300
Given the function
f(x)=xsin(pi/2sqrt(x)),
this is the conclusion of the Mean Value Theorem for a value c in (1,4).
What is
f'(c)=-1/3?
400
This is the slope of the tangent line of
f(x)=x^2sinpix-3x
at x=1.
What is
-pi-3?
400
If the rate of change of a quantity over the closed interval [-1,5] is given by
f'(x)=xe^(x^2),
then the net change of the quantity over the interval is this.
What is
1/2e^25-1/2e?
400
This is the solution to
lim_(h->0)((4+h)^3-4^3)/h
What is 48?
400
This is the solution to the differential equation
dy/dx=(x^2-1)/y.
What is
y=sqrt(2/3x^3-2x+C.
400
This is the relative minimum of the function
f'(x)=(-x^3+4x-2)/sqrt(x^2+1).
What is
x=0.539?
500
This is the derivative of
f(x)=ln((2x-3)/(x+8)).
What is
f'(x)=2/(2x-3)-1/(x+8)?
500
This is the solution to
f(x)=intx*sqrt(1/6x^2+5)dx.
What is
f(x)=2(1/6x^2+5)^(3/2)+C?
500
This is the solution to
lim_(h->0)((x+h)^9sin(x+h)^2-x^9sinx^2)/h.
What is
x^8(9sinx^2+2x^2cosx^2)?
500
This is the solution to the differential equation
dy/dx=-x/(y*e^(x^2/2).
What is
sqrt(2e^(-x^2/2)+C).
500
Let R be the region in the first quadrant bounded by the graphs of
f(x)=5x-x^2
and
g(x)=2^x-1.
Find the area of the region R.
What is 15.91 square units?