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AP Calculus AB Flashcards: Estimating Limit Values From Graphs

Study Estimating Limit Values From Graphs in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Estimating Limit Values From Graphs, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Tap or drag to reveal answer

ANSWER

The constant value. Constant functions have the same value everywhere.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Answer: The constant value. Constant functions have the same value everywhere.

Flashcard 2: What is the limit of $\lim_{x \to -a} f(x)$ for $f(x) = x^2$ ?

Answer: $a^2$ . $(-a)^2 = a^2$ for any real number $a$ .

Flashcard 3: What is $\lim_{x \to 0} \frac{1}{x}$ ?

Answer: Does not exist; approaches $\infty$ as $x \to 0^+$ and $-\infty$ as $x \to 0^-$ . Left and right limits differ, so the limit doesn't exist.

Flashcard 4: What is the graphical significance of $\lim_{x \to c} f(x) = \infty$ ?

Answer: Vertical asymptote at $x = c$ . Infinite limits create vertical asymptotes on graphs.

Flashcard 5: What does $\lim_{x \to 0} e^{-x}$ approach?

Answer:

$e^{-x}$ approaches $e^0 = 1$ as $x \to 0$ .

Flashcard 6: What is indicated by $\lim_{x \to c} f(x) \neq f(c)$ ?

Answer: A removable discontinuity at $x = c$ . The limit exists but doesn't equal the function value.

Flashcard 7: What does $\lim_{x \to a} f(x)$ equal if $f(x)$ is linear?

Answer: $f(a)$ . Linear functions are continuous everywhere.

Flashcard 8: Identify $\lim_{x \to 0^-} \frac{1}{x}$ .

Answer: $-\infty$ . Approaching from the left gives negative infinity.

Flashcard 9: Identify $\lim_{x \to -\infty} f(x)$ from the graph.

Answer: The left horizontal asymptote value if it exists. Check where the graph levels off on the left side.

Flashcard 10: What does $\lim_{x \to a} f(x) = f(a)$ imply?

Answer: Function is continuous at $x = a$ . The limit equals the function value at that point.

Flashcard 11: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Answer: The constant value. Constant functions have the same value everywhere.

Flashcard 12: How do you denote the limit of $f(x)$ as $x$ approaches $a$ from the right?

Answer: $\lim_{x \to a^+} f(x)$ . The plus superscript denotes right-hand limit notation.

Flashcard 13: What is the behavior of $f(x)$ near $x = a$ if $\lim_{x \to a} f(x) = L$ ?

Answer: Approaches $L$ as $x$ approaches $a$ . This describes the fundamental limit behavior.

Flashcard 14: What is $\lim_{x \to 0} \sin(\frac{1}{x})$ ?

Answer: The limit does not exist due to oscillation. The function oscillates infinitely near $x = 0$ .

Flashcard 15: What does a continuous graph imply about limits at all points?

Answer: Limits exist and equal the function values. Continuity guarantees limit existence everywhere.

Flashcard 16: Determine $\lim_{x \to \infty} \frac{1}{x^2}$ using a graph.

Answer:

$\frac{1}{x^2}$ approaches $0$ as $x$ becomes large.

Flashcard 17: Which term describes the behavior of $f(x)$ as $x \to 2^+$ ?

Answer: Right-hand limit. The $+$ superscript indicates approach from the right side.

Flashcard 18: Determine $\lim_{x \to 0} x^2$ using a graph.

Answer:

The function $x^2$ approaches $0$ as $x$ approaches $0$ .

Flashcard 19: What is the result of $\lim_{x \to 2^-} f(x)$ if $f(x)$ jumps at $x = 2$ ?

Answer: The $y$ -value approaching from the left of $x = 2$ . One-sided limits can exist even with jump discontinuities.

Flashcard 20: Determine $\lim_{x \to 4} f(x)$ if $f(x)$ is continuous at $x = 4$ .

Answer: $f(4)$ . Continuity means the limit equals the function value.

Flashcard 21: How does $\lim_{x \to 0} \frac{1}{x^2}$ behave?

Answer: Approaches $\infty$ . $\frac{1}{x^2}$ grows without bound near $x = 0$ .

Flashcard 22: What is $\lim_{x \to c} f(x)$ if $f(x)$ is undefined at $x = c$ ?

Answer: The $y$ -value $f(x)$ approaches as $x$ nears $c$ . Limits exist even when function values don't.

Flashcard 23: State the notation for the left-hand limit of $f(x)$ at $x = a$ .

Answer: $\lim_{x \to a^-} f(x)$ . Standard notation for left-hand limits.

Flashcard 24: State the meaning of $\lim_{x \to c} f(x) = L$ .

Answer: $f(x)$ approaches $L$ as $x$ approaches $c$ . This is the formal definition of a limit.

Flashcard 25: How do you denote the limit of $f(x)$ as $x$ approaches $a$ on a graph?

Answer: $\lim_{x \to a} f(x)$ . Standard mathematical notation for limits.

Flashcard 26: What does $\lim_{x \to c^-} f(x)$ represent?

Answer: Limit from the left of $c$ . The minus superscript indicates approach from the left.

Flashcard 27: What does $\lim_{x \to \infty} \frac{1}{x}$ equal?

Answer:

$\frac{1}{x}$ approaches $0$ as $x$ becomes large.

Flashcard 28: How do you find $\lim_{x \to \infty} f(x)$ from a graph?

Answer: Identify the horizontal asymptote if it exists. Look for the horizontal line the graph approaches.

Flashcard 29: What is the limit as $x \to \infty$ of a linear function?

Answer: Does not exist; increases or decreases without bound. Linear functions grow without bound at infinity.

Flashcard 30: State the vertical asymptote implication for limits.

Answer: Limit does not exist at the vertical asymptote. Vertical asymptotes prevent limit existence.

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AP Calculus AB Flashcards: Estimating Limit Values From Graphs

Study Estimating Limit Values From Graphs in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Estimating Limit Values From Graphs, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Tap or drag to reveal answer

ANSWER

The constant value. Constant functions have the same value everywhere.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Answer: The constant value. Constant functions have the same value everywhere.

Flashcard 2: What is the limit of $\lim_{x \to -a} f(x)$ for $f(x) = x^2$ ?

Answer: $a^2$ . $(-a)^2 = a^2$ for any real number $a$ .

Flashcard 3: What is $\lim_{x \to 0} \frac{1}{x}$ ?

Answer: Does not exist; approaches $\infty$ as $x \to 0^+$ and $-\infty$ as $x \to 0^-$ . Left and right limits differ, so the limit doesn't exist.

Flashcard 4: What is the graphical significance of $\lim_{x \to c} f(x) = \infty$ ?

Answer: Vertical asymptote at $x = c$ . Infinite limits create vertical asymptotes on graphs.

Flashcard 5: What does $\lim_{x \to 0} e^{-x}$ approach?

Answer:

$e^{-x}$ approaches $e^0 = 1$ as $x \to 0$ .

Flashcard 6: What is indicated by $\lim_{x \to c} f(x) \neq f(c)$ ?

Answer: A removable discontinuity at $x = c$ . The limit exists but doesn't equal the function value.

Flashcard 7: What does $\lim_{x \to a} f(x)$ equal if $f(x)$ is linear?

Answer: $f(a)$ . Linear functions are continuous everywhere.

Flashcard 8: Identify $\lim_{x \to 0^-} \frac{1}{x}$ .

Answer: $-\infty$ . Approaching from the left gives negative infinity.

Flashcard 9: Identify $\lim_{x \to -\infty} f(x)$ from the graph.

Answer: The left horizontal asymptote value if it exists. Check where the graph levels off on the left side.

Flashcard 10: What does $\lim_{x \to a} f(x) = f(a)$ imply?

Answer: Function is continuous at $x = a$ . The limit equals the function value at that point.

Flashcard 11: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Answer: The constant value. Constant functions have the same value everywhere.

Flashcard 12: How do you denote the limit of $f(x)$ as $x$ approaches $a$ from the right?

Answer: $\lim_{x \to a^+} f(x)$ . The plus superscript denotes right-hand limit notation.

Flashcard 13: What is the behavior of $f(x)$ near $x = a$ if $\lim_{x \to a} f(x) = L$ ?

Answer: Approaches $L$ as $x$ approaches $a$ . This describes the fundamental limit behavior.

Flashcard 14: What is $\lim_{x \to 0} \sin(\frac{1}{x})$ ?

Answer: The limit does not exist due to oscillation. The function oscillates infinitely near $x = 0$ .

Flashcard 15: What does a continuous graph imply about limits at all points?

Answer: Limits exist and equal the function values. Continuity guarantees limit existence everywhere.

Flashcard 16: Determine $\lim_{x \to \infty} \frac{1}{x^2}$ using a graph.

Answer:

$\frac{1}{x^2}$ approaches $0$ as $x$ becomes large.

Flashcard 17: Which term describes the behavior of $f(x)$ as $x \to 2^+$ ?

Answer: Right-hand limit. The $+$ superscript indicates approach from the right side.

Flashcard 18: Determine $\lim_{x \to 0} x^2$ using a graph.

Answer:

The function $x^2$ approaches $0$ as $x$ approaches $0$ .

Flashcard 19: What is the result of $\lim_{x \to 2^-} f(x)$ if $f(x)$ jumps at $x = 2$ ?

Answer: The $y$ -value approaching from the left of $x = 2$ . One-sided limits can exist even with jump discontinuities.

Flashcard 20: Determine $\lim_{x \to 4} f(x)$ if $f(x)$ is continuous at $x = 4$ .

Answer: $f(4)$ . Continuity means the limit equals the function value.

Flashcard 21: How does $\lim_{x \to 0} \frac{1}{x^2}$ behave?

Answer: Approaches $\infty$ . $\frac{1}{x^2}$ grows without bound near $x = 0$ .

Flashcard 22: What is $\lim_{x \to c} f(x)$ if $f(x)$ is undefined at $x = c$ ?

Answer: The $y$ -value $f(x)$ approaches as $x$ nears $c$ . Limits exist even when function values don't.

Flashcard 23: State the notation for the left-hand limit of $f(x)$ at $x = a$ .

Answer: $\lim_{x \to a^-} f(x)$ . Standard notation for left-hand limits.

Flashcard 24: State the meaning of $\lim_{x \to c} f(x) = L$ .

Answer: $f(x)$ approaches $L$ as $x$ approaches $c$ . This is the formal definition of a limit.

Flashcard 25: How do you denote the limit of $f(x)$ as $x$ approaches $a$ on a graph?

Answer: $\lim_{x \to a} f(x)$ . Standard mathematical notation for limits.

Flashcard 26: What does $\lim_{x \to c^-} f(x)$ represent?

Answer: Limit from the left of $c$ . The minus superscript indicates approach from the left.

Flashcard 27: What does $\lim_{x \to \infty} \frac{1}{x}$ equal?

Answer:

$\frac{1}{x}$ approaches $0$ as $x$ becomes large.

Flashcard 28: How do you find $\lim_{x \to \infty} f(x)$ from a graph?

Answer: Identify the horizontal asymptote if it exists. Look for the horizontal line the graph approaches.

Flashcard 29: What is the limit as $x \to \infty$ of a linear function?

Answer: Does not exist; increases or decreases without bound. Linear functions grow without bound at infinity.

Flashcard 30: State the vertical asymptote implication for limits.

Answer: Limit does not exist at the vertical asymptote. Vertical asymptotes prevent limit existence.

Opening subject page...

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

All flashcards

Flashcard 1: How do you find lim⁡x→5f(x)\lim_{x \to 5} f(x)limx→5​f(x) if f(x)f(x)f(x) is constant?

Flashcard 2: What is the limit of lim⁡x→−af(x)\lim_{x \to -a} f(x)limx→−a​f(x) for f(x)=x2f(x) = x^2f(x)=x2?

Flashcard 3: What is lim⁡x→01x\lim_{x \to 0} \frac{1}{x}limx→0​x1​?

Flashcard 4: What is the graphical significance of lim⁡x→cf(x)=∞\lim_{x \to c} f(x) = \inftylimx→c​f(x)=∞?

Flashcard 5: What does lim⁡x→0e−x\lim_{x \to 0} e^{-x}limx→0​e−x approach?

Flashcard 6: What is indicated by lim⁡x→cf(x)≠f(c)\lim_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 7: What does lim⁡x→af(x)\lim_{x \to a} f(x)limx→a​f(x) equal if f(x)f(x)f(x) is linear?

Flashcard 8: Identify lim⁡x→0−1x\lim_{x \to 0^-} \frac{1}{x}limx→0−​x1​.

Flashcard 9: Identify lim⁡x→−∞f(x)\lim_{x \to -\infty} f(x)limx→−∞​f(x) from the graph.

Flashcard 10: What does lim⁡x→af(x)=f(a)\lim_{x \to a} f(x) = f(a)limx→a​f(x)=f(a) imply?

Flashcard 11: How do you find lim⁡x→5f(x)\lim_{x \to 5} f(x)limx→5​f(x) if f(x)f(x)f(x) is constant?

Flashcard 12: How do you denote the limit of f(x)f(x)f(x) as xxx approaches aaa from the right?

Flashcard 13: What is the behavior of f(x)f(x)f(x) near x=ax = ax=a if lim⁡x→af(x)=L\lim_{x \to a} f(x) = Llimx→a​f(x)=L?

Flashcard 14: What is lim⁡x→0sin⁡(1x)\lim_{x \to 0} \sin(\frac{1}{x})limx→0​sin(x1​)?

Flashcard 15: What does a continuous graph imply about limits at all points?

Flashcard 16: Determine lim⁡x→∞1x2\lim_{x \to \infty} \frac{1}{x^2}limx→∞​x21​ using a graph.

Flashcard 17: Which term describes the behavior of f(x)f(x)f(x) as x→2+x \to 2^+x→2+?

Flashcard 18: Determine lim⁡x→0x2\lim_{x \to 0} x^2limx→0​x2 using a graph.

Flashcard 19: What is the result of lim⁡x→2−f(x)\lim_{x \to 2^-} f(x)limx→2−​f(x) if f(x)f(x)f(x) jumps at x=2x = 2x=2?

Flashcard 20: Determine lim⁡x→4f(x)\lim_{x \to 4} f(x)limx→4​f(x) if f(x)f(x)f(x) is continuous at x=4x = 4x=4.

Flashcard 21: How does lim⁡x→01x2\lim_{x \to 0} \frac{1}{x^2}limx→0​x21​ behave?

Flashcard 22: What is lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) if f(x)f(x)f(x) is undefined at x=cx = cx=c?

Flashcard 23: State the notation for the left-hand limit of f(x)f(x)f(x) at x=ax = ax=a.

Flashcard 24: State the meaning of lim⁡x→cf(x)=L\lim_{x \to c} f(x) = Llimx→c​f(x)=L.

Flashcard 25: How do you denote the limit of f(x)f(x)f(x) as xxx approaches aaa on a graph?

Flashcard 26: What does lim⁡x→c−f(x)\lim_{x \to c^-} f(x)limx→c−​f(x) represent?

Flashcard 27: What does lim⁡x→∞1x\lim_{x \to \infty} \frac{1}{x}limx→∞​x1​ equal?

Flashcard 28: How do you find lim⁡x→∞f(x)\lim_{x \to \infty} f(x)limx→∞​f(x) from a graph?

Flashcard 29: What is the limit as x→∞x \to \inftyx→∞ of a linear function?

Flashcard 30: State the vertical asymptote implication for limits.

Opening subject page...

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Estimating Limit Values From Graphs

All flashcards

Flashcard 1: How do you find lim⁡x→5f(x)\lim_{x \to 5} f(x)limx→5​f(x) if f(x)f(x)f(x) is constant?

Flashcard 2: What is the limit of lim⁡x→−af(x)\lim_{x \to -a} f(x)limx→−a​f(x) for f(x)=x2f(x) = x^2f(x)=x2?

Flashcard 3: What is lim⁡x→01x\lim_{x \to 0} \frac{1}{x}limx→0​x1​?

Flashcard 4: What is the graphical significance of lim⁡x→cf(x)=∞\lim_{x \to c} f(x) = \inftylimx→c​f(x)=∞?

Flashcard 5: What does lim⁡x→0e−x\lim_{x \to 0} e^{-x}limx→0​e−x approach?

Flashcard 6: What is indicated by lim⁡x→cf(x)≠f(c)\lim_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 7: What does lim⁡x→af(x)\lim_{x \to a} f(x)limx→a​f(x) equal if f(x)f(x)f(x) is linear?

Flashcard 8: Identify lim⁡x→0−1x\lim_{x \to 0^-} \frac{1}{x}limx→0−​x1​.

Flashcard 9: Identify lim⁡x→−∞f(x)\lim_{x \to -\infty} f(x)limx→−∞​f(x) from the graph.

Flashcard 10: What does lim⁡x→af(x)=f(a)\lim_{x \to a} f(x) = f(a)limx→a​f(x)=f(a) imply?

Flashcard 11: How do you find lim⁡x→5f(x)\lim_{x \to 5} f(x)limx→5​f(x) if f(x)f(x)f(x) is constant?

Flashcard 12: How do you denote the limit of f(x)f(x)f(x) as xxx approaches aaa from the right?

Flashcard 13: What is the behavior of f(x)f(x)f(x) near x=ax = ax=a if lim⁡x→af(x)=L\lim_{x \to a} f(x) = Llimx→a​f(x)=L?

Flashcard 14: What is lim⁡x→0sin⁡(1x)\lim_{x \to 0} \sin(\frac{1}{x})limx→0​sin(x1​)?

Flashcard 15: What does a continuous graph imply about limits at all points?

Flashcard 16: Determine lim⁡x→∞1x2\lim_{x \to \infty} \frac{1}{x^2}limx→∞​x21​ using a graph.

Flashcard 17: Which term describes the behavior of f(x)f(x)f(x) as x→2+x \to 2^+x→2+?

Flashcard 18: Determine lim⁡x→0x2\lim_{x \to 0} x^2limx→0​x2 using a graph.

Flashcard 19: What is the result of lim⁡x→2−f(x)\lim_{x \to 2^-} f(x)limx→2−​f(x) if f(x)f(x)f(x) jumps at x=2x = 2x=2?

Flashcard 20: Determine lim⁡x→4f(x)\lim_{x \to 4} f(x)limx→4​f(x) if f(x)f(x)f(x) is continuous at x=4x = 4x=4.

Flashcard 21: How does lim⁡x→01x2\lim_{x \to 0} \frac{1}{x^2}limx→0​x21​ behave?

Flashcard 22: What is lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) if f(x)f(x)f(x) is undefined at x=cx = cx=c?

Flashcard 23: State the notation for the left-hand limit of f(x)f(x)f(x) at x=ax = ax=a.

Flashcard 24: State the meaning of lim⁡x→cf(x)=L\lim_{x \to c} f(x) = Llimx→c​f(x)=L.

Flashcard 25: How do you denote the limit of f(x)f(x)f(x) as xxx approaches aaa on a graph?

Flashcard 26: What does lim⁡x→c−f(x)\lim_{x \to c^-} f(x)limx→c−​f(x) represent?

Flashcard 27: What does lim⁡x→∞1x\lim_{x \to \infty} \frac{1}{x}limx→∞​x1​ equal?

Flashcard 28: How do you find lim⁡x→∞f(x)\lim_{x \to \infty} f(x)limx→∞​f(x) from a graph?

Flashcard 29: What is the limit as x→∞x \to \inftyx→∞ of a linear function?

Flashcard 30: State the vertical asymptote implication for limits.

Flashcard 1: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Flashcard 2: What is the limit of $\lim_{x \to -a} f(x)$ for $f(x) = x^2$ ?

Flashcard 3: What is $\lim_{x \to 0} \frac{1}{x}$ ?

Flashcard 4: What is the graphical significance of $\lim_{x \to c} f(x) = \infty$ ?

Flashcard 5: What does $\lim_{x \to 0} e^{-x}$ approach?

Flashcard 6: What is indicated by $\lim_{x \to c} f(x) \neq f(c)$ ?

Flashcard 7: What does $\lim_{x \to a} f(x)$ equal if $f(x)$ is linear?

Flashcard 8: Identify $\lim_{x \to 0^-} \frac{1}{x}$ .

Flashcard 9: Identify $\lim_{x \to -\infty} f(x)$ from the graph.

Flashcard 10: What does $\lim_{x \to a} f(x) = f(a)$ imply?

Flashcard 11: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Flashcard 12: How do you denote the limit of $f(x)$ as $x$ approaches $a$ from the right?

Flashcard 13: What is the behavior of $f(x)$ near $x = a$ if $\lim_{x \to a} f(x) = L$ ?

Flashcard 14: What is $\lim_{x \to 0} \sin(\frac{1}{x})$ ?

Flashcard 16: Determine $\lim_{x \to \infty} \frac{1}{x^2}$ using a graph.

Flashcard 17: Which term describes the behavior of $f(x)$ as $x \to 2^+$ ?

Flashcard 18: Determine $\lim_{x \to 0} x^2$ using a graph.

Flashcard 19: What is the result of $\lim_{x \to 2^-} f(x)$ if $f(x)$ jumps at $x = 2$ ?

Flashcard 20: Determine $\lim_{x \to 4} f(x)$ if $f(x)$ is continuous at $x = 4$ .

Flashcard 21: How does $\lim_{x \to 0} \frac{1}{x^2}$ behave?

Flashcard 22: What is $\lim_{x \to c} f(x)$ if $f(x)$ is undefined at $x = c$ ?

Flashcard 23: State the notation for the left-hand limit of $f(x)$ at $x = a$ .

Flashcard 24: State the meaning of $\lim_{x \to c} f(x) = L$ .

Flashcard 25: How do you denote the limit of $f(x)$ as $x$ approaches $a$ on a graph?

Flashcard 26: What does $\lim_{x \to c^-} f(x)$ represent?

Flashcard 27: What does $\lim_{x \to \infty} \frac{1}{x}$ equal?

Flashcard 28: How do you find $\lim_{x \to \infty} f(x)$ from a graph?

Flashcard 29: What is the limit as $x \to \infty$ of a linear function?

Flashcard 1: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Flashcard 2: What is the limit of $\lim_{x \to -a} f(x)$ for $f(x) = x^2$ ?

Flashcard 3: What is $\lim_{x \to 0} \frac{1}{x}$ ?

Flashcard 4: What is the graphical significance of $\lim_{x \to c} f(x) = \infty$ ?

Flashcard 5: What does $\lim_{x \to 0} e^{-x}$ approach?

Flashcard 6: What is indicated by $\lim_{x \to c} f(x) \neq f(c)$ ?

Flashcard 7: What does $\lim_{x \to a} f(x)$ equal if $f(x)$ is linear?

Flashcard 8: Identify $\lim_{x \to 0^-} \frac{1}{x}$ .

Flashcard 9: Identify $\lim_{x \to -\infty} f(x)$ from the graph.

Flashcard 10: What does $\lim_{x \to a} f(x) = f(a)$ imply?

Flashcard 11: How do you find $\lim_{x \to 5} f(x)$ if $f(x)$ is constant?

Flashcard 12: How do you denote the limit of $f(x)$ as $x$ approaches $a$ from the right?

Flashcard 13: What is the behavior of $f(x)$ near $x = a$ if $\lim_{x \to a} f(x) = L$ ?

Flashcard 14: What is $\lim_{x \to 0} \sin(\frac{1}{x})$ ?

Flashcard 16: Determine $\lim_{x \to \infty} \frac{1}{x^2}$ using a graph.

Flashcard 17: Which term describes the behavior of $f(x)$ as $x \to 2^+$ ?

Flashcard 18: Determine $\lim_{x \to 0} x^2$ using a graph.

Flashcard 19: What is the result of $\lim_{x \to 2^-} f(x)$ if $f(x)$ jumps at $x = 2$ ?

Flashcard 20: Determine $\lim_{x \to 4} f(x)$ if $f(x)$ is continuous at $x = 4$ .

Flashcard 21: How does $\lim_{x \to 0} \frac{1}{x^2}$ behave?

Flashcard 22: What is $\lim_{x \to c} f(x)$ if $f(x)$ is undefined at $x = c$ ?

Flashcard 23: State the notation for the left-hand limit of $f(x)$ at $x = a$ .

Flashcard 24: State the meaning of $\lim_{x \to c} f(x) = L$ .

Flashcard 25: How do you denote the limit of $f(x)$ as $x$ approaches $a$ on a graph?

Flashcard 26: What does $\lim_{x \to c^-} f(x)$ represent?

Flashcard 27: What does $\lim_{x \to \infty} \frac{1}{x}$ equal?

Flashcard 28: How do you find $\lim_{x \to \infty} f(x)$ from a graph?

Flashcard 29: What is the limit as $x \to \infty$ of a linear function?