Functions
Limits
Derivatives
Antiderivatives
Applications
100
A toolkit function whose derivative is always 0.
What is a constant function
100
A function f is continuous at a if the limit as x approaches a of f(x) equals f(a).
What is Continuity
100
The limit definition of the derivative
What is ask Marin because it's too complicated to type on here
100
General form of antiderivative. Hint: Use F(x) as antiderivative
What is F(x) + C
100
The equation of a line that is parallel to f(x) = 3x+4 and goes through the point (4,2)
What is f(x) = 3x-10
200
The output of one function is used as the input of another.
What is composition of functions
200
The 3 types of Discontinuity
What is Removable, Infinite, and Jump Discontinuity
200
If f(x) = 1/x, f'(1) = ?. Use limit definition.
What is -1
200
Antiderivative of 2x^3+7x
What is (1/2)x^4+(7/2)x^2+C
200
This allows you to find local maximums and minimums of a function
What is the First Derivative Test
300
A function in which the formula used depends upon the part of the domain the input lies in.
What is a piecewise function
300
Suppose that the function f is continuous on the closed interval [a,b] and let N be any number between f(a) and f(b), where f(a) does not equal f(b). Then there exists some value c in (a,b) such that f(c) = N.
What is the Intermediate Value Theorem
300
Derivative of f(x) = (2x+3)(sqrt(2x))
What is f'(x) = 2(sqrt(2x))+[(2x+3)/(sqrt(2x))]
300
Antiderivative method of the "Chain Rule"
What is "U-Substitution"
300
Find the linearization of f(x) = sqrt(x+8) at x=1 and use it to approximate sqrt(9.02) and sqrt(8.98)
What is sqrt(9.02) = (18.02/6) ~ 3.003333 and sqrt(8.98) = (17.98/6) ~ 2.996667
400
Transform the toolkit function f(x) = x^2 by moving it 4 units to the left, 2 units up, and horizontally stretching it by a factor of 2.
What is f(x) = 0.5(x + 4)^2+2
400
The limit as x approaches 0 of f(x) = 1/x
What is DNE
400
Derivative of f(x) = (sqrt(4x^2-5))/(x^3)
What is too complicated to type in this so ask Marin
400
Antiderivative of 2x(sqrt(x^2+5))
What is (2/3)(x^2+5)^(3/2)+C
400
The area under the function f(x) = 2x(x^2+1)^2 over the interval [0,1]
What is 7/3
500
The inverse of f(x) = (2x-5)/(x^2+3)
What is f^(-1)(x) = (3x+5)/(2-4x)
500
The limit as x approaches infinity of f(x) = (3x^2+2x-1)/(x^2-x+5)
What is 3
500
Derivative of 2x-y^2 = 3xy
What is dy/dx = (2-3y)/(3x+2y)
500
Theorem that says you can evaluate an antiderivative with bounds [a,b]
What is Fundamental Theorem of Calculus Part 2 (FTC2)
500
The optimal height of a ball thrown off the roof of a 20 meter building if thrown at 22 meters/second. Assume gravity to be 10 meters/second^2.
What is 46 meters
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