AP Calculus AB Practice Limits (1.2 - 1.3)

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a limit in calculus?
Back
A limit is a value that a function approaches as the input approaches some value.
2.
FLASHCARD QUESTION
Front
Define the notation \( \lim_{x \to c} f(x) \).
Back
It represents the limit of the function \( f(x) \) as \( x \) approaches the value \( c \).
3.
FLASHCARD QUESTION
Front
What does it mean if \( \lim_{x \to c} f(x) = DNE \)?
Back
It means that the limit does not exist; the function does not approach a specific value as \( x \) approaches \( c \).
4.
FLASHCARD QUESTION
Front
How do you find \( \lim_{x \to c^-} f(x) \)?
Back
Evaluate the limit of \( f(x) \) as \( x \) approaches \( c \) from the left side.
5.
FLASHCARD QUESTION
Front
How do you find \( \lim_{x \to c^+} f(x) \)?
Back
Evaluate the limit of \( f(x) \) as \( x \) approaches \( c \) from the right side.
6.
FLASHCARD QUESTION
Front
What is the limit of a constant function?
Back
The limit of a constant function is the constant itself, regardless of the value of \( x \).
7.
FLASHCARD QUESTION
Front
What is the limit of \( f(x) = \frac{1}{x} \) as \( x \to 0 \)?
Back
The limit does not exist (DNE) because the function approaches \( \infty \) from the right and \( -\infty \) from the left.
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