Limits and Continuity
When a function f(x) is defined at all x-values
What is continuous?
The definition of ___ is defined as limx->a(f(x)-f(a)/(x-a))
What is derivative?
A function's ___ is a seperate function that the derivative can be taken of to get the original function
What is antiderivative?
Parametric functions will most often be graphed in terms of this variable
What is t?
Founder of a rule used in evaluating limits, which allows you to simplify the limit if the limit is in one of two indeterminate forms
Who is L'Hopital?
The limit as x approaches infinity of a constantly increasing function
What is infinity?
The differentiation process done in the form of d/dx f(g(x)) = f'(g(x))g'(x)
What is chain rule?
A process of estimating the area under a curve using rectangles of equal length
What are Riemann-sums?
For a parametric function, the x-derivative listed with the y-derivative will give the velocity ___ of the function
What is a vector?
Founder of a type of general term series that involves a function being taken to the nth derivative, factorials, and x centered at 0
Who is Maclaurin?
What a function is if the limit from the right does not equal the limit from the left at a point
What is discontinuous?
The differentiation process done in the form of d/dx f(x)g(x) = f'(x)g(x) + g'(x)f(x)
What is product rule?
A type of integral where one or both endpoints are infinity
What is an improper integral?
The square root of the sum of the x and y derivatives squared of a parametric function gives the ___ of the velocity vector
What is a magnitude?
Founder of a solving method for differential equations that involves approximating the function with steps of equal size
Who is Euler?
What you can find using this form of equation (f(a)-f(b))/(a-b)
What is average rate of change?
The derivative of a function at a point where its tangent line is horizontal
What is 0?
A process of solving an integral problem by interchanging part or all of the integral with a function with a known antiderivative
What is u-substitution?
Graphed in polar coordinates, the point (4, 2𝝅/3) will be up and ___ from the origin
Widely considered to be one of the founders of Calculus
Who is Isaac Newton?
The type of discontinuity where the limit exists and is equal from both sides
What is jump discontinuity?
For a function to be decreasing and positively accelerating, its second derivative must be positive and its first derivative must be ___
What is negative?
For all even functions, an integral from negative c to positive c will equal ___
What is 0?
What is theta?
Founder of the calculus journal check, daily fact, and basket squirrel
Who is Ms. Contreras?