Imagine This:
i4 equals this value.
What is 1?
To find the derivatives of polynomials, an easy method is to use this rule.
What is the power rule?
These are the solutions to the function -3x(x-5)(x+4).
What are 5, 0, and -4?
This is the limit of the constant n as x approaches the constant a.
What is n?
DAILY DOUBLE
This shape has the lowest surface area to volume ratio of any possible 3d shape.
What is a sphere?
(i - 2)(i + 2) equals this real number.
What is -5?
This is the derivative of lnx.
This is the factored version of x2 + 2x + 1.
When taking a limit, if the answer is in the form of 0/0, infinity/infinity, 00, infinityinfinity, etc., then the limit is in this form.
What is indeterminate form?
This shape is created from the path Mr. Barnhart takes after jumping out of a tree into a pile of mattresses to escape a squirrel.
What is a parabola?
Also acceptable: Quadratic
This is the first function in physics that uses the imaginary unit to describe the real word. This equation also has the same namesake of a famous cat found in a box.
What is Schrodinger's Equation?
The quotient rule has this formula. (Assume f(x)/g(x) is the original function.)
What is
f'(x)g(x) - f(x)g'(x)
________________
g(x)2
When factoring a polynomial, this should be factored first.
What are coefficients?
This rule that literally translates to "The Hospital" cannot be used when taking the derivative of a function.
What is L'Hopital's rule?
This study of surfaces and shapes can prove that a doughnut and a straw have the same amount of holes.
This is the polar form of a complex number.
What is reix?
r is the distance from the origin.
x is the angle in radians.
This operation is also called the anti-derivative, and it finds the area under a curve.
What is an integral?
When a graph "bounces" against the x-axis, the solution must have this type of multiplicity.
What is an even multiplicity?
The limit of 1/x as x approaches 0 from the positive side is this.
What is infinity?
This is the volume of a cone with a height of 9 and a base radius of 2. (in terms of pi)
What is 12pi?
DAILY DOUBLE
Imaginary numbers were first used to find the real solutions of this type of polynomial that is called "depressed" when the coefficient in front of the x2 term is 0.
What is a cubic?
Also acceptable: third degree polynomial.
This is the nth derivative of xex.
What is nex + xex?
When a real function such as x2 + 1 has no real solutions, then the problem will exclusively contain these types of factors.
What are complex conjugate pairs?
The limit as h approaches 0 of [(x+h)2 - (x)2]/h is the same as taking the derivative of this function.
What is x2?
This "standard" form of geometry is only separated from other types of geometries by Euclid's 5th axiom. In this geometry, the angles of a triangle add up to 180 degrees.
What is Euclidean Geometry?