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AP Calculus AB
Unit 1: Limits and Continuity
1.1 Introducing Calculus: Connecting Graphs and Rates of Change
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Cards (51)
What is the mathematical discipline that studies continuous change and rates of change?
Calculus
Differential calculus focuses on accumulation and areas under curves.
False
The key concept in integral calculus is the
integral
The key concept in differential calculus is the
derivative
In the formal definition of a limit, the symbols ε and δ represent small positive
numbers
Calculus studies continuous change and rates of
change
What is the primary tool used in integral calculus?
Integration techniques
What is the defining characteristic of a continuous function?
No jumps or breaks
What are asymptotes in a graph?
Lines graph approaches
Local extrema are points where the function reaches a local maximum or
minimum
Local extrema occur where the rate of change switches
direction
Calculus deals with rates of change and
continuous functions
.
True
What are local extrema of a function's graph?
Peaks and valleys
What does an increasing function indicate about its rate of change?
Positive slope
Match the graph feature with its relationship to the rate of change:
Constant Portion ↔️ Zero rate of change
Increasing Portion ↔️ Positive rate of change
Decreasing Portion ↔️ Negative rate of change
The formula for average rate of change is
(f(b) - f(a)) / (b - a)
The acceleration of a car speeding up from rest is a
variable rate of change
.
True
Differential calculus deals with rates of change and slopes of
curves
Match the branch of calculus with its key concept:
Differential Calculus ↔️ Derivative
Integral Calculus ↔️ Integral
Integration techniques are tools used in differential calculus.
False
Limits are used to analyze the behavior of
functions
as they approach a specific point.
True
The limit of f(x) = x + 2 as x approaches 3 is 5.
True
What is the focus of differential calculus in terms of function behavior?
Slopes of curves
The key concepts in the formal definition of a limit include ε, δ, |x - c|, and
|f(x) - L|
A function is increasing if it rises from left to
right
What is the definition of a continuous function in terms of its graph?
No jumps or breaks
What is the graphical representation of asymptotes?
Dashed lines
Match the graph feature with its relationship to the rate of change:
Increasing Portion ↔️ Positive
Decreasing Portion ↔️ Negative
Constant Portion ↔️ Zero
What can differential calculus be used to find in physics?
Velocity
Asymptotes are lines that the graph approaches but never
touches
When a function is increasing, its rate of change is
positive
What does the average rate of change measure over an interval?
Function change
What is an example of a constant rate in real life?
Steady car speed
What is an example of a constant rate of change in finance?
Fixed interest rate
What is the primary focus of integral calculus?
Areas under curves
Which real-life application uses differential calculus?
Optimization
What is the focus of differential calculus?
Rates of change
What does the formal definition of a limit describe?
Value a function approaches
Match the definition of a limit with its description:
Formal Definition ↔️ For every ε > 0, there exists δ > 0 such that if 0 < |x - c| < δ, then |f(x) - L| < ε
Informal Definition ↔️ Describes the value a function approaches as x gets arbitrarily close to a point
Differential calculus is used to find integrals.
False
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