What is The highest point over the entire domain of a function or relation?
100
Define trapezoid rule.
What is A method for approximating a definite integral using linear approximations of f. The trapezoids are drawn as shown below. The bases are vertical lines?
200
the derivative of a function is equal to what?
What is the slope of the tangent line?
200
Define the Fundamental Theorem of Calculus.
What is Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b]?
200
lim -x-3/x^2+x+1
x->(3/2)
What is (-18/19)?
200
Define asymptote.
What is A line or curve that the graph of a relation approaches more and more closely the further the graph is followed?
200
Define quotient rule.
What is a formula for the derivative of the quotient of two functions?
300
Derive 4x^3 + 7x^2 + 2x
What is 12x^2 + 14x + 2?
300
Define the Second Fundamental Theorem of Calculus.
What is Let f be a real-valued function defined on a closed interval [a, b] that admits an antiderivative F on [a, b]. That is, f and F are functions such that for all x in [a, b]?
300
lim sin(x)
x->pi
What is 0?
300
Define critical point.
What is A point (x, y) on the graph of a function at which the derivative is either 0 or undefined. A critical point will often be a minimum or maximum, but it may be neither?
300
Define Mean Value Theorem.
What is A major theorem of calculus that relates values of a function to a value of its derivative. Essentially the theorem states that for a "nice" function, there is a tangent line parallel to any secant line?
400
How do you perform the product rule?
What is the first times the derivative of the second plus the second times the derivative of the first?
400
Define Integral.
What is a function of which a given function is the derivative, i.e., which yields that function when differentiated, and which may express the area under the curve of a graph of the function?
400
lim 5
x->-1
What is 5?
400
Define inflection point.
What is A point at which a curve changes from concave up to concave down, or vice-versa?
400
Define Parameter.
What is the independent variable or variables in a set of parametric equations?
500
Define the term "tangent line".
What is A tangent line is a straight line that touches a function at only one point. The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point?
500
Integrate ∫(-1)^(3) ((2x+1)^2)dx
What is 57 1/3?
500
lim (x^3-x^2-4)
x->2
What is 0?
500
Define solid of revolution.
A solid that is obtained by rotating a plane figure in space about an axis coplanar to the figure. The axis may not intersect the figure?
500
Define second derivative test.
What is a method for determining whether a critical point is a relative minimum or maximum?