If a limit is in indeterminate form, this rule can come in handy.
What is L'Hopital's Rule?
100
It is the magnitude of the vector <6,7>.
What is the square root of 85?
100
This number is equivalent to the area under the curve y=e^(-x/2) in the first quadrant.
What is 2?
100
With functions that take the form r=acos(θ) and r=asin(nθ), these kinds of polar curves are often compared to flowers.
What are Rose Curves?
100
A series diverges if its limit as it approaches infinity does not equal this number.
What is zero?
200
This is the truncation error of the geometric series 1/(1-x^2).
What is x^8/(1-x^2)?
200
It is the formula for the acceleration vector.
What is
200
The integral of a function f(x) from negative infinity to infinity can also be represented by this formula.
What is the integral of f(x) from negative infinity to a constant C plus the integral of f(x) from the same constant to infinity?
200
If (r,θ) was a point on a graph, these two points would represent (r,θ) reflected over the x-axis.
What are (r,-θ) and (-r,180-θ)?
200
The name given to an alternating series that diverges when the alternating component is removed.
What is conditionally convergent?
300
If the point (1,2) and dy/dx=x+1, Euler's Method with increments of .1 should give you this value of y for x=1.2.
What is 2.41?
300
These types of functions are just another way of representing vectors.
What are parametric functions?
300
For the integral of the function 1/(x^p) from 1 to infinity, where p>1, this formula can be used to determine what value the function converges to.
What is 1/(p-1)?
300
It's the polar-rectangular conversion formula for x.
What is x=rcos(θ)?
300
The interval of convergence for the series n=0Σinfinity (x^4n)/(n!)^4
What is all values of x?
400
This formula represents the slope of a polar curve.
What is dy/dx= f'(θ)sin(θ)+f(θ)cos(θ)/f'cos(θ)-f(θ)sin(θ)?
400
If the position of a particle is given by the parametric equations x(t)=1-t^3 and y(t)=t^2-4, this is the coordinates of the acceleration at a time when the particle is at rest.
What is (0,2)?
400
This is the area under the curve y=1/(x^.5) from x=0 to x=1.
What is 2?
400
It's the area enclosed by the limacon r=2-cos(θ)
What is (9*Pi)/2?
400
It's the radius of convergence for the series n=0Σinfinity (x+5)^n.
What is 1?
500
The ideal motion of a projectile can be written as two parametric equations. This equation represents the y-component of the projectile's motion.
What is y=|initial velocity|sin(α)t-.5gt^2+initial y-postion?
500
This is the dot product of the vectors <-1,5> and <2,8>.
What is 38?
500
Once the integral 2dx/(x^2)-1 from x=negative infinity to x=-2 is evaluated, this answer is reached.
What is the ln of 3?
500
This function is the Cartesian version of the polar equation (r^2)sin(2θ)=10
What is y=5/x?
500
It's the interval of convergence of the series n=1Σinfinity (x-3)^n/2n.