AP Calculus AB: Chapter 2 Test
This flashcard set focuses on interpreting limits from graphs and numerical data. It emphasizes identifying points where limits exist or fail, understanding graphical discontinuities, and estimating rates of change like acceleration using values from a table.
What is the limit of the function in the graph at x = 4?
2
Key Terms
What is the limit of the function in the graph at x = 4?
2
What is the limit of the function in the graph at x = 4?
The limit does not exist.
For what value(s) of x does the function in the graph not have a limit?
4 and 6
The velocity of the cyclist in feet per second as a function of time is given in the table below.
t 0 1 2 3 4
f(t) 10 20 24 22 18
The approximate acceleration (rate of change of the velocity with respect to time) of the cyclist at time t = 2 seconds is which of the following?
1 ft / s^2
Suppose that lim x→−1 3−4x=7.
Find the largest value of δ such that |(3−4x)−7|
0.0005
Suppose that lim x→a f(x)=32,
lim x→a g(x)=68, and lim x→a h(x)=10. Then lim x→a f(x)+g(x)/h(x) is equal to which of the following?
10
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| Term | Definition |
|---|---|
What is the limit of the function in the graph at x = 4? | 2 |
What is the limit of the function in the graph at x = 4? | The limit does not exist. |
For what value(s) of x does the function in the graph not have a limit? | 4 and 6 |
The velocity of the cyclist in feet per second as a function of time is given in the table below. The approximate acceleration (rate of change of the velocity with respect to time) of the cyclist at time t = 2 seconds is which of the following? | 1 ft / s^2 |
Suppose that lim x→−1 3−4x=7. Find the largest value of δ such that |(3−4x)−7| | 0.0005 |
lim x→a g(x)=68, and lim x→a h(x)=10. Then lim x→a f(x)+g(x)/h(x) is equal to which of the following? | 10 |
f(x)={3x, x<2 | 6 |
f(x)=√x^2−4 Evaluate lim x→2− f(x). | The limit doesn’t exist |
Consider the function, f(t)= t^2+1 if −1≤t<1 −t+1 if 1≤t<2 −1 if t>2 The set of points in the domain of f at which f is continuous is which of the following? | [−1, 1), (1, 2), (2, ∞) |
Determine, if it exists, lim x→3 sin (x−3)/√x+6 . | 0 |
Determine, if it exists, lim x→ −2 x−2/x^2−4. | The limit does not exist. |
Determine, if it exists, lim x→2 x^2−5x+6 / x^2−4. | -1/4 |
Determine, if it exists, lim x→3 x^2−5x+6 / x^2−6x+9. | The limit does not exist. |
Determine, if it exists, lim x→2 x−5+6/x / x−4/x. | -1/4 |
Determine, if it exists, lim x→3 1/x−5/x^2+6/x^3 / x−6/x^2 + 9x^3. | The limit does not exist. |
Determine, if it exists, lim x→0 x^2−x / √x+1 −1. | -2 |
Determine, if it exists, limx→2 √x+7 −3 / x^2−4x+4. | The limit does not exist. |
Evaluate the following as true or false.The notation lim x→2 f(x)=5 states that the limit of the function f at x=5 is 2. | false |
What is the limit of the function in the graph at x = 4? | The limit does not exist. |
For what value(s) of x does the function given in the graph not have a limit? | x = 4 |