AP Calculus AB Flashcards: Introducing Calculus: Can Change Occur at an Instant?
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
If you try to calculate a car's average speed over a time interval of zero, what mathematical problem do you encounter?
You encounter an undefined value because the calculation for average rate of change requires dividing by the change in time, which is zero.
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If you try to calculate a car's average speed over a time interval of zero, what mathematical problem do you encounter?
You encounter an undefined value because the calculation for average rate of change requires dividing by the change in time, which is zero.
What fundamental tool does calculus use to understand and model dynamic change?
Calculus uses limits to understand and model dynamic change.
What is the relationship between limits and instantaneous rates of change?
Limits are the tool used to formalize the idea of an instantaneous rate of change by analyzing average rates of change over infinitesimally small intervals.
Why is the average rate of change undefined at a single point?
The average rate of change is undefined at a single point because the change in the independent variable would be zero, leading to division by zero.
What concept allows us to define an instantaneous rate of change based on average rates of change?
The limit concept allows us to define instantaneous rate of change in terms of average rates of change.
How does calculus allow for the study of change that occurs at an instant?
Calculus uses limits to analyze the trend of average rates of change as the interval of measurement approaches zero, thus defining change at an instant.
How is the rate of change at a single instant interpreted in calculus?
The rate of change at an instant is interpreted in terms of the average rates of change over intervals containing that instant.
To find the slope of a curve at a single point, we can't use the standard slope formula. How does calculus solve this?
Calculus uses the limit concept to find the slope by interpreting it as the limit of the average rates of change (slopes of secant lines) over intervals that shrink around that point.
Instantaneous Rate of Change
The rate of change at a particular instant, defined using the limit concept in terms of average rates of change over progressively smaller intervals.
Average Rate of Change
A rate that is calculated by dividing the change in one variable by the change in another over a non-zero interval.