Limits & Continuity
The value a function approaches as x approaches a number.
What is a Limit?
The instantaneous rate of change of a function.
What is a Derivative?
This symbol (∫) is used to represent this calculus concept.
What is an Integral?
The derivative of position with respect to time.
This theorem guarantees a y-value between f(a) and f(b) if f is continuous on [a, b].
What is Intermediate Value Theorem (IVT)?
A function is this if the limit exists and equals the function's value at that point.
What is Continuous?
Do I Di - Rule used to differentiate a composition of functions.
What is the Chain Rule?
The reverse process of taking a derivative.
What is the Antiderivative?
The derivative of velocity.
What is Acceleration?
This theorem says a continuous function on [a, b] will reach a maximum and minimum.
What is Extreme Value Theorem (EVT)?
A break, jump, or hole in the graph of a function.
What is a Discontinuity
Using derivatives to relate the rates at which different quantities change.
What is Related Rates?
The process of using rectangles to approximate the area under a curve.
What is Riemann Sum?
When velocity and acceleration have opposite signs, the function is...
What is Slowing Down?
If a function is continuous and differentiable on [a, b], this theorem ensures a point where the instantaneous rate of change equals the average rate of change.
What is Mean Value Theorem (MVT)?
A line x=a where the function’s values grow without bound (approach infinity or negative infinity) as the input approaches a
What is a Vertical Asymptote?
Using the derivative to approximate values of a function near a point.
What is Linear Approximation?
A technique evaluate integrals and find antiderivatives through substitution.
What is U-Substitution?
The point where an object changes direction from right to left or vice versa.
What is a Turning Point?
This theorem states that taking the derivative of an accumulated area gives you back the original function.
What is Fundamental Theorem of Calculus Part 1 (FTC1)?
A line y=b that the graph of a function approaches as x goes to positive or negative infinity.
What is a Horizontal Asymptote?
Finding the derivative of an equation where y is not solved for explicitly by differentiating both sides and using the chain rule.
What is Implicit Differentiation?
The process of finding the antiderivative of a function.
What is Indefinite Integration?
Net change in position over time interval [a, b].
What is Displacement?
This theorems states that the total accumulated change of a quantity over an interval equals the difference in the original quantity’s values at the endpoints.
What is Fundamental Theorem of Calculus – Part 2 (FTC2)?