Derivatives
Integrals
Rules and Theorems
Sequences and Series
Miscellaneous Math
100
This man's method is used to approximate values of a function based on the differential equation and a given point.
Who is Euler?
100
This is the expression ∫(1/x²)dx once it has been evaluated
What is -1/x + C?
100
A function satisfies the Mean Value Theorem if it is this, meaning it is defined at all values in the interval
What is continuous?
100
A series which eventually becomes a finite number is known as this
What is convergent?
100
The standard form of this conic section is x²/a² - y²/b² = 1
What is a hyperbola?
200
This is the second derivative with respect to x of the equation y = 2x⁷-4x⁴+7x³-2
What is 84x⁵-48x²+42x?
200
This type of integral is one such as the definite integral from 1 to 3 of the function f(x) = 5x/(x²-6x+8)
What is improper?
200
This man's theorem is a version of the MVT when the slope of the secant line is 0
Who is Rolle?
200
If a series has terms that cancel out, leaving only a few terms, then it is known as this.
What is telescoping?
200
This is csc(π/6)
What is 2?
300
One would use this test to determine where an inflection point lies
What is the second derivative test?
300
∫ln(x)dx from 1 to e is this
What is 2e-1?
300
Using the FTC, what is d/dt of ∫t-3 from 4x³ to 0
What is (4x³-3)(-12x²)?
300
The first 5 terms of the Taylor Series for this function are 1-x²/2!+x⁴/4!-x⁶/6!+x⁸/8!
What is cos(x)?
300
This term describes a line segment with both endpoints on a circle (but not the diameter)
What is a chord?
400
This is the maximum area of the rectangle with vertices on the x-axis and the function y = -x²+3
What is 4?
400
This is the average value of y = 1/(1+x²) on the interval [0, 1]
What is π/4?
400
When used on an decreasing concave down function, this rule will be the lowest of all four numerical methods for approximating definite integrals
What is the right-hand rule?
400
In the formula for Lagrange error, the M represents this
What is the maximum value of the derivative?
400
If the tangent of an angle is 3/4, then this is secant theta
What is 5/4?
500
If the surface area of a cube is changing at a rate of 4 m²/s, when the side length is 2, the volume is changing at a rate of this number m³/s
What is 2?
500
This is the integral expression when you rotate the function y=x^2 +3 bounded by x=3 and the x-axis around the y-axis using the washer method
What is 2π∫(x(x^2+3))dx from 0 to 3?
500
The error for this rule is shown here: http://upload.wikimedia.org/math/2/1/6/216244f9b5fb5f2e17b31e8a5efc5898.png
What is Simpson's Rule?
500
This is P(4) of 5e^x²
What is 5+5x²+5x⁴/2+5x⁶/6?
500
This woman is the best calculus teacher in the whole world
Who is Ms. Hochrein?
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