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Limits
Derivatives
Integrals
Rates
Vocab
100
The limit of x^2 + 5x - 8 as x approaches 12
What is 196?
100
derivative of 5x^2
What is 10x?
100
The integral of 3x^2
What is x^3 + C?
100
Given the position function f(x)=x^2, the velocity at x=4 is
What is 8?
100
The instantaneous rate of change of the function at a or the slope of the tangent line at a.
What is the derivative of f at a?
200
The limit of (x^2-x-6)/(x-3) as x approaches 3
What is 5?
200
derivative of e^ax
What is (e^ax)*(da/dx)?
200
The integral of sin(x) from -pi to pi
What is 0?
200
Given the position function x(t)=3x^3-15, the speed at t=4 is
What is increasing?
200
A number c in an open (a,b) interval where the derivative is zero or does not exist.
What is Critical Number c?
300
The limit of sin(17x)/x as x approaches 0
What is 17?
300
derivative of ln(x)
What is 1/x?
300
The integral of x
What is (x^2)/2 + C?
300
The rate of change of the rate of change in position is this
What is acceleration?
300
The name of this test: a) If the first derivative changes from negative to positive at c then the function has a relative minimum at c. b) If the first derivative changes from positive to negative at c then the function has a relative minimum at c.
What is the first derivative test?
400
The limit of the piecewise function: f(x)= x+3, x>2 12(x^2)-42, x< or = 2 as x approaches 2
What is DNE?
400
Derivative of (6x(3x^2))
What is 54x^2?
400
The integral of x^2 + 5
What is (x^3)/3 + 5x + C
400
Given V=4/3(Pi)r^3, the change in volume with respect to time is this
What is dv/dt=4(pi)r^2(dr/dt)?
400
The name of this test: a) If the second derivative is positive on an interval I then the function is Concave Up on I. b) If the second derivative is negative on an interval I the function is Concave down on I.
What is the Concavity Test?
500
The limit of (e^x - ln(e) +6)/(5x-2) as x approaches 0
What is -3?
500
the second derivative of ln((e^x)x)
What is -1/(x^2)?
500
The integral of (2x + 2)(e^(x^2) + 2x + 3)dx.
What is (e^(x^2) + 2x + 3) + C?
500
This man's first law uses related rates to state that an object with no force acting on it, will move in a straight at a constant speed. (He is often considered the father of calculus)
Who is Sir Issac Newton?
500
Name this point: f: Is a point where the concavity of f changes. f': Is a point where f' changes from increasing to decreasing or decreasing to increasing. f": Is a point where f" changes from positive to negative or negative to positive.
What is a point of inflection?