AP Calculus BC Flashcards: Estimating Limit Values From Graphs

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

AP Calculus BC

Estimating Limit Values From Graphs

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QUESTION

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Identify $\text{lim}_{x \to 1^+} f(x)$ from a graph approaching value 4.

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ANSWER

Right-hand limit reads $y$ -value approached from positive side.

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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 BC.

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.

All flashcards

Flashcard 1: Identify $\text{lim}_{x \to 1^+} f(x)$ from a graph approaching value 4.

Answer:

Right-hand limit reads $y$ -value approached from positive side.

Flashcard 2: What does it mean if $\text{lim}_{x \to c} f(x) = L$ ?

Answer: As $x$ approaches $c$ , $f(x)$ approaches $L$ . Standard limit notation expressing function behavior near point $c$ .

Flashcard 3: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that levels off at $y = 9$ .

Answer:

Horizontal asymptote at $y = 9$ as $x$ increases.

Flashcard 4: What does $\text{lim}_{x \to 0^-} f(x) = 3$ indicate about $f(x)$ ?

Answer: $f(x)$ approaches 3 as $x$ approaches 0 from the left. Left-hand limit describes approach from negative direction.

Flashcard 5: What is the condition for a limit to exist at $x = c$ ?

Answer: $\text{lim}_{x \to c^-} f(x) = \text{lim}_{x \to c^+} f(x)$ . Both one-sided limits must exist and be equal.

Flashcard 6: Estimate $\text{lim}_{x \to 3^-} f(x)$ if the graph shows $f(x)$ approaching 6.

Answer:

Left-hand limit reads $y$ -value from negative approach.

Flashcard 7: If $\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)$ , what can be said about $\text{lim}_{x \to c} f(x)$ ?

Answer: The limit does not exist. Two-sided limit requires both one-sided limits to be equal.

Flashcard 8: Estimate $\text{lim}_{x \to 4^-} f(x)$ from a graph showing $f(x)$ approaches 2.

Answer:

Left-hand limit reads $y$ -value approached from negative side.

Flashcard 9: Estimate $\text{lim}_{x \to -2} f(x)$ from the graph if $f(x)$ approaches 5.

Answer:

Read the $y$ -value the graph approaches at $x = -2$ .

Flashcard 10: What is $\text{lim}_{x \to \text{infinity}} f(x)$ if the graph levels off at 7?

Answer:

Horizontal asymptotes show end behavior as $x \to \infty$ .

Flashcard 11: What does the graph of $f(x)$ show if $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Answer: A point discontinuity at $x = c$ . When limit exists but doesn't equal function value at that point.

Flashcard 12: Estimate $\lim_{x \to -3^+} f(x)$ if the graph shows $f(x)$ approaching 5.

Answer:

Right-hand limit reads $y$ -value from positive approach.

Flashcard 13: If $\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)$ , what can be said about $\text{lim}_{x \to c} f(x)$ ?

Answer: The limit does not exist. Two-sided limit requires both one-sided limits to be equal.

Flashcard 14: Estimate $\text{lim}_{x \to -3^+} f(x)$ if the graph shows $f(x)$ approaching 5.

Answer:

Right-hand limit reads $y$ -value from positive approach.

Flashcard 15: What does it mean if $\text{lim}_{x \to c} f(x) = L$ ?

Answer: As $x$ approaches $c$ , $f(x)$ approaches $L$ . Standard limit notation expressing function behavior near point $c$ .

Flashcard 16: Estimate $\text{lim}_{x \to -\text{infinity}} f(x)$ if the graph approaches 0.

Answer:

Read where graph heads as $x$ decreases without bound.

Flashcard 17: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that approaches $y = 0$ .

Answer:

Horizontal asymptote shows end behavior approaching zero.

Flashcard 18: Estimate $\text{lim}_{x \to 0} f(x)$ from a graph with a vertical asymptote at $x = 0$ .

Answer: The limit does not exist. Vertical asymptotes cause limits to not exist.

Flashcard 19: If a graph has a vertical asymptote at $x = 1$ , what is $\text{lim}_{x \to 1} f(x)$ ?

Answer: The limit does not exist. Vertical asymptotes mean function goes to $\pm\infty$ , so limit doesn't exist.

Flashcard 20: What is implied if $\text{lim}_{x \to \text{infinity}} f(x) = L$ ?

Answer: The graph of $f(x)$ approaches $y = L$ as $x$ increases. Describes horizontal asymptote behavior at infinity.

Flashcard 21: Estimate $\lim_{x \to 5} f(x)$ if graph approaches different values from left and right.

Answer: The limit does not exist. Different one-sided limits mean the two-sided limit doesn't exist.

Flashcard 22: What is $\text{lim}_{x \to 3} f(x)$ if the graph shows a hole at $x = 3$ ?

Answer: The $y$ -value the graph approaches as $x$ approaches 3. Holes don't affect limits; read where the curve would go.

Flashcard 23: What is indicated by $\text{lim}_{x \to c} f(x) = L$ on a continuous graph?

Answer: The function value $f(c) = L$ . Continuous functions have limits equal to function values.

Flashcard 24: What is the condition for a limit to exist at $x = c$ ?

Answer: $\text{lim}_{x \to c^-} f(x) = \text{lim}_{x \to c^+} f(x)$ . Both one-sided limits must exist and be equal.

Flashcard 25: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that levels off at $y = 9$ .

Answer:

Horizontal asymptote at $y = 9$ as $x$ increases.

Flashcard 26: Which notation represents the limit of $f(x)$ as $x$ approaches 0 from the left?

Answer: $\text{lim}_{x \to 0^-} f(x)$ . The minus sign indicates approaching from the negative (left) side.

Flashcard 27: Determine the limit if $\text{lim}_{x \to 0^-} f(x) = -4$ and $\text{lim}_{x \to 0^+} f(x) = 4$ .

Answer: The limit does not exist. Unequal one-sided limits mean no two-sided limit exists.

Flashcard 28: Identify the limit of $f(x)$ as $x$ approaches 2 from the right on a graph.

Answer: The $y$ -value that $f(x)$ approaches as $x$ approaches 2 from the right. Read the $y$ -coordinate where the curve heads as $x$ nears 2 from positive side.

Flashcard 29: Determine the limit if $\text{lim}_{x \to 0^-} f(x) = -4$ and $\text{lim}_{x \to 0^+} f(x) = 4$ .

Answer: The limit does not exist. Unequal one-sided limits mean no two-sided limit exists.

Flashcard 30: If a graph has a vertical asymptote at $x = 1$ , what is $\text{lim}_{x \to 1} f(x)$ ?

Answer: The limit does not exist. Vertical asymptotes mean function goes to $\pm\infty$ , so limit doesn't exist.

Flashcard 31: Find $\text{lim}_{x \to 2} f(x)$ if the graph is continuous at $x = 2$ and $f(2) = 8$ .

Answer:

For continuous functions, limit equals function value.

Flashcard 32: What is $\text{lim}_{x \to \text{infinity}} f(x)$ if the graph levels off at 7?

Answer:

Horizontal asymptotes show end behavior as $x \to \infty$ .

Flashcard 33: What is $\text{lim}_{x \to 3} f(x)$ if the graph shows a hole at $x = 3$ ?

Answer: The $y$ -value the graph approaches as $x$ approaches 3. Holes don't affect limits; read where the curve would go.

Flashcard 34: Estimate $\text{lim}_{x \to 0} f(x)$ from a graph with a vertical asymptote at $x = 0$ .

Answer: The limit does not exist. Vertical asymptotes cause limits to not exist.

Flashcard 35: Estimate $\text{lim}_{x \to 2} f(x)$ from a graph where $f(x)$ approaches $-3$ .

Answer: -3. Read the $y$ -value the graph approaches at $x = 2$ .

Flashcard 36: Estimate $\text{lim}_{x \to 5} f(x)$ if graph approaches different values from left and right.

Answer: The limit does not exist. Different one-sided limits mean the two-sided limit doesn't exist.

Flashcard 37: Which notation represents the limit of $f(x)$ as $x$ approaches 0 from the left?

Answer: $\text{lim}_{x \to 0^-} f(x)$ . The minus sign indicates approaching from the negative (left) side.

Flashcard 38: Estimate $\text{lim}_{x \to -\text{infinity}} f(x)$ if the graph approaches 0.

Answer:

Read where graph heads as $x$ decreases without bound.

Flashcard 39: Determine $\lim_{x \to 0} f(x)$ if graph shows $f(x)$ approaches 3 from both sides.

Answer:

When both one-sided limits equal the same value.

Flashcard 40: Estimate $\text{lim}_{x \to -2} f(x)$ from the graph if $f(x)$ approaches 5.

Answer:

Read the $y$ -value the graph approaches at $x = -2$ .

Flashcard 41: What is the implication if $\text{lim}_{x \to c} f(x)$ exists but $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Answer: A removable discontinuity at $x = c$ . Limit exists but function is not continuous at that point.

Flashcard 42: Estimate $\text{lim}_{x \to 2} f(x)$ from a graph where $f(x)$ approaches $-3$ .

Answer: -3. Read the $y$ -value the graph approaches at $x = 2$ .

Flashcard 43: What is the implication if $\text{lim}_{x \to c} f(x)$ exists but $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Answer: A removable discontinuity at $x = c$ . Limit exists but function is not continuous at that point.

Flashcard 44: Estimate $\text{lim}_{x \to 7} f(x)$ if the graph shows a removable discontinuity at $x = 7$ .

Answer: The $y$ -value the graph approaches, not the point at the discontinuity. Removable discontinuities don't affect limit values.

Flashcard 45: Estimate $\lim_{x \to 3^-} f(x)$ if the graph shows $f(x)$ approaching 6.

Answer:

Left-hand limit reads $y$ -value from negative approach.

Flashcard 46: What is implied if $\text{lim}_{x \to \text{infinity}} f(x) = L$ ?

Answer: The graph of $f(x)$ approaches $y = L$ as $x$ increases. Describes horizontal asymptote behavior at infinity.

Flashcard 47: Find $\text{lim}_{x \to 2} f(x)$ if the graph is continuous at $x = 2$ and $f(2) = 8$ .

Answer:

For continuous functions, limit equals function value.

Flashcard 48: Estimate $\lim_{x \to \infty} f(x)$ from a graph that approaches $y = 0$ .

Answer: $0$ . Horizontal asymptote shows end behavior approaching zero.

Flashcard 49: Identify $\text{lim}_{x \to 1^+} f(x)$ from a graph approaching value 4.

Answer:

Right-hand limit reads $y$ -value approached from positive side.

Flashcard 50: What does the graph of $f(x)$ show if $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Answer: A point discontinuity at $x = c$ . When limit exists but doesn't equal function value at that point.

Flashcard 51: Determine $\text{lim}_{x \to 0} f(x)$ if graph shows $f(x)$ approaches 3 from both sides.

Answer:

When both one-sided limits equal the same value.

Flashcard 52: Estimate $\text{lim}_{x \to 7} f(x)$ if the graph shows a removable discontinuity at $x = 7$ .

Answer: The $y$ -value the graph approaches, not the point at the discontinuity. Removable discontinuities don't affect limit values.

Flashcard 53: What is indicated by $\text{lim}_{x \to c} f(x) = L$ on a continuous graph?

Answer: The function value $f(c) = L$ . Continuous functions have limits equal to function values.

Flashcard 54: Identify the limit of $f(x)$ as $x$ approaches 2 from the right on a graph.

Answer: The $y$ -value that $f(x)$ approaches as $x$ approaches 2 from the right. Read the $y$ -coordinate where the curve heads as $x$ nears 2 from positive side.

AP Calculus BC Flashcards: Estimating Limit Values From Graphs

Estimating Limit Values From Graphs

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Identify limx→1+f(x)\text{lim}_{x \to 1^+} f(x)limx→1+​f(x) from a graph approaching value 4.

Flashcard 2: What does it mean if limx→cf(x)=L\text{lim}_{x \to c} f(x) = Llimx→c​f(x)=L?

Flashcard 3: Estimate limx→infinityf(x)\text{lim}_{x \to \text{infinity}} f(x)limx→infinity​f(x) from a graph that levels off at y=9y = 9y=9.

Flashcard 4: What does limx→0−f(x)=3\text{lim}_{x \to 0^-} f(x) = 3limx→0−​f(x)=3 indicate about f(x)f(x)f(x)?

Flashcard 5: What is the condition for a limit to exist at x=cx = cx=c?

Flashcard 6: Estimate limx→3−f(x)\text{lim}_{x \to 3^-} f(x)limx→3−​f(x) if the graph shows f(x)f(x)f(x) approaching 6.

Flashcard 7: If limx→c−f(x)≠limx→c+f(x)\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)limx→c−​f(x)=limx→c+​f(x), what can be said about limx→cf(x)\text{lim}_{x \to c} f(x)limx→c​f(x)?

Flashcard 8: Estimate limx→4−f(x)\text{lim}_{x \to 4^-} f(x)limx→4−​f(x) from a graph showing f(x)f(x)f(x) approaches 2.

Flashcard 9: Estimate limx→−2f(x)\text{lim}_{x \to -2} f(x)limx→−2​f(x) from the graph if f(x)f(x)f(x) approaches 5.

Flashcard 10: What is limx→infinityf(x)\text{lim}_{x \to \text{infinity}} f(x)limx→infinity​f(x) if the graph levels off at 7?

Flashcard 11: What does the graph of f(x)f(x)f(x) show if limx→cf(x)≠f(c)\text{lim}_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 12: Estimate lim⁡x→−3+f(x)\lim_{x \to -3^+} f(x)limx→−3+​f(x) if the graph shows f(x)f(x)f(x) approaching 5.

Flashcard 13: If limx→c−f(x)≠limx→c+f(x)\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)limx→c−​f(x)=limx→c+​f(x), what can be said about limx→cf(x)\text{lim}_{x \to c} f(x)limx→c​f(x)?

Flashcard 14: Estimate limx→−3+f(x)\text{lim}_{x \to -3^+} f(x)limx→−3+​f(x) if the graph shows f(x)f(x)f(x) approaching 5.

Flashcard 15: What does it mean if limx→cf(x)=L\text{lim}_{x \to c} f(x) = Llimx→c​f(x)=L?

Flashcard 16: Estimate limx→−infinityf(x)\text{lim}_{x \to -\text{infinity}} f(x)limx→−infinity​f(x) if the graph approaches 0.

Flashcard 17: Estimate limx→infinityf(x)\text{lim}_{x \to \text{infinity}} f(x)limx→infinity​f(x) from a graph that approaches y=0y = 0y=0.

Flashcard 18: Estimate limx→0f(x)\text{lim}_{x \to 0} f(x)limx→0​f(x) from a graph with a vertical asymptote at x=0x = 0x=0.

Flashcard 19: If a graph has a vertical asymptote at x=1x = 1x=1, what is limx→1f(x)\text{lim}_{x \to 1} f(x)limx→1​f(x)?

Flashcard 20: What is implied if limx→infinityf(x)=L\text{lim}_{x \to \text{infinity}} f(x) = Llimx→infinity​f(x)=L?

Flashcard 21: Estimate lim⁡x→5f(x)\lim_{x \to 5} f(x)limx→5​f(x) if graph approaches different values from left and right.

Flashcard 22: What is limx→3f(x)\text{lim}_{x \to 3} f(x)limx→3​f(x) if the graph shows a hole at x=3x = 3x=3?

Flashcard 23: What is indicated by limx→cf(x)=L\text{lim}_{x \to c} f(x) = Llimx→c​f(x)=L on a continuous graph?

Flashcard 24: What is the condition for a limit to exist at x=cx = cx=c?

Flashcard 25: Estimate limx→infinityf(x)\text{lim}_{x \to \text{infinity}} f(x)limx→infinity​f(x) from a graph that levels off at y=9y = 9y=9.

Flashcard 26: Which notation represents the limit of f(x)f(x)f(x) as xxx approaches 0 from the left?

Flashcard 27: Determine the limit if limx→0−f(x)=−4\text{lim}_{x \to 0^-} f(x) = -4limx→0−​f(x)=−4 and limx→0+f(x)=4\text{lim}_{x \to 0^+} f(x) = 4limx→0+​f(x)=4.

Flashcard 28: Identify the limit of f(x)f(x)f(x) as xxx approaches 2 from the right on a graph.

Flashcard 29: Determine the limit if limx→0−f(x)=−4\text{lim}_{x \to 0^-} f(x) = -4limx→0−​f(x)=−4 and limx→0+f(x)=4\text{lim}_{x \to 0^+} f(x) = 4limx→0+​f(x)=4.

Flashcard 30: If a graph has a vertical asymptote at x=1x = 1x=1, what is limx→1f(x)\text{lim}_{x \to 1} f(x)limx→1​f(x)?

Flashcard 31: Find limx→2f(x)\text{lim}_{x \to 2} f(x)limx→2​f(x) if the graph is continuous at x=2x = 2x=2 and f(2)=8f(2) = 8f(2)=8.

Flashcard 32: What is limx→infinityf(x)\text{lim}_{x \to \text{infinity}} f(x)limx→infinity​f(x) if the graph levels off at 7?

Flashcard 33: What is limx→3f(x)\text{lim}_{x \to 3} f(x)limx→3​f(x) if the graph shows a hole at x=3x = 3x=3?

Flashcard 34: Estimate limx→0f(x)\text{lim}_{x \to 0} f(x)limx→0​f(x) from a graph with a vertical asymptote at x=0x = 0x=0.

Flashcard 35: Estimate limx→2f(x)\text{lim}_{x \to 2} f(x)limx→2​f(x) from a graph where f(x)f(x)f(x) approaches −3-3−3.

Flashcard 36: Estimate limx→5f(x)\text{lim}_{x \to 5} f(x)limx→5​f(x) if graph approaches different values from left and right.

Flashcard 37: Which notation represents the limit of f(x)f(x)f(x) as xxx approaches 0 from the left?

Flashcard 38: Estimate limx→−infinityf(x)\text{lim}_{x \to -\text{infinity}} f(x)limx→−infinity​f(x) if the graph approaches 0.

Flashcard 39: Determine lim⁡x→0f(x)\lim_{x \to 0} f(x)limx→0​f(x) if graph shows f(x)f(x)f(x) approaches 3 from both sides.

Flashcard 40: Estimate limx→−2f(x)\text{lim}_{x \to -2} f(x)limx→−2​f(x) from the graph if f(x)f(x)f(x) approaches 5.

Flashcard 41: What is the implication if limx→cf(x)\text{lim}_{x \to c} f(x)limx→c​f(x) exists but limx→cf(x)≠f(c)\text{lim}_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 42: Estimate limx→2f(x)\text{lim}_{x \to 2} f(x)limx→2​f(x) from a graph where f(x)f(x)f(x) approaches −3-3−3.

Flashcard 43: What is the implication if limx→cf(x)\text{lim}_{x \to c} f(x)limx→c​f(x) exists but limx→cf(x)≠f(c)\text{lim}_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 44: Estimate limx→7f(x)\text{lim}_{x \to 7} f(x)limx→7​f(x) if the graph shows a removable discontinuity at x=7x = 7x=7.

Flashcard 45: Estimate lim⁡x→3−f(x)\lim_{x \to 3^-} f(x)limx→3−​f(x) if the graph shows f(x)f(x)f(x) approaching 6.

Flashcard 46: What is implied if limx→infinityf(x)=L\text{lim}_{x \to \text{infinity}} f(x) = Llimx→infinity​f(x)=L?

Flashcard 47: Find limx→2f(x)\text{lim}_{x \to 2} f(x)limx→2​f(x) if the graph is continuous at x=2x = 2x=2 and f(2)=8f(2) = 8f(2)=8.

Flashcard 48: Estimate lim⁡x→∞f(x)\lim_{x \to \infty} f(x)limx→∞​f(x) from a graph that approaches y=0y = 0y=0.

Flashcard 49: Identify limx→1+f(x)\text{lim}_{x \to 1^+} f(x)limx→1+​f(x) from a graph approaching value 4.

Flashcard 50: What does the graph of f(x)f(x)f(x) show if limx→cf(x)≠f(c)\text{lim}_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)?

Flashcard 51: Determine limx→0f(x)\text{lim}_{x \to 0} f(x)limx→0​f(x) if graph shows f(x)f(x)f(x) approaches 3 from both sides.

Flashcard 52: Estimate limx→7f(x)\text{lim}_{x \to 7} f(x)limx→7​f(x) if the graph shows a removable discontinuity at x=7x = 7x=7.

Flashcard 53: What is indicated by limx→cf(x)=L\text{lim}_{x \to c} f(x) = Llimx→c​f(x)=L on a continuous graph?

Flashcard 54: Identify the limit of f(x)f(x)f(x) as xxx approaches 2 from the right on a graph.

Flashcard 1: Identify $\text{lim}_{x \to 1^+} f(x)$ from a graph approaching value 4.

Flashcard 2: What does it mean if $\text{lim}_{x \to c} f(x) = L$ ?

Flashcard 3: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that levels off at $y = 9$ .

Flashcard 4: What does $\text{lim}_{x \to 0^-} f(x) = 3$ indicate about $f(x)$ ?

Flashcard 5: What is the condition for a limit to exist at $x = c$ ?

Flashcard 6: Estimate $\text{lim}_{x \to 3^-} f(x)$ if the graph shows $f(x)$ approaching 6.

Flashcard 7: If $\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)$ , what can be said about $\text{lim}_{x \to c} f(x)$ ?

Flashcard 8: Estimate $\text{lim}_{x \to 4^-} f(x)$ from a graph showing $f(x)$ approaches 2.

Flashcard 9: Estimate $\text{lim}_{x \to -2} f(x)$ from the graph if $f(x)$ approaches 5.

Flashcard 10: What is $\text{lim}_{x \to \text{infinity}} f(x)$ if the graph levels off at 7?

Flashcard 11: What does the graph of $f(x)$ show if $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Flashcard 12: Estimate $\lim_{x \to -3^+} f(x)$ if the graph shows $f(x)$ approaching 5.

Flashcard 13: If $\text{lim}_{x \to c^-} f(x) \neq \text{lim}_{x \to c^+} f(x)$ , what can be said about $\text{lim}_{x \to c} f(x)$ ?

Flashcard 14: Estimate $\text{lim}_{x \to -3^+} f(x)$ if the graph shows $f(x)$ approaching 5.

Flashcard 15: What does it mean if $\text{lim}_{x \to c} f(x) = L$ ?

Flashcard 16: Estimate $\text{lim}_{x \to -\text{infinity}} f(x)$ if the graph approaches 0.

Flashcard 17: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that approaches $y = 0$ .

Flashcard 18: Estimate $\text{lim}_{x \to 0} f(x)$ from a graph with a vertical asymptote at $x = 0$ .

Flashcard 19: If a graph has a vertical asymptote at $x = 1$ , what is $\text{lim}_{x \to 1} f(x)$ ?

Flashcard 20: What is implied if $\text{lim}_{x \to \text{infinity}} f(x) = L$ ?

Flashcard 21: Estimate $\lim_{x \to 5} f(x)$ if graph approaches different values from left and right.

Flashcard 22: What is $\text{lim}_{x \to 3} f(x)$ if the graph shows a hole at $x = 3$ ?

Flashcard 23: What is indicated by $\text{lim}_{x \to c} f(x) = L$ on a continuous graph?

Flashcard 24: What is the condition for a limit to exist at $x = c$ ?

Flashcard 25: Estimate $\text{lim}_{x \to \text{infinity}} f(x)$ from a graph that levels off at $y = 9$ .

Flashcard 26: Which notation represents the limit of $f(x)$ as $x$ approaches 0 from the left?

Flashcard 27: Determine the limit if $\text{lim}_{x \to 0^-} f(x) = -4$ and $\text{lim}_{x \to 0^+} f(x) = 4$ .

Flashcard 28: Identify the limit of $f(x)$ as $x$ approaches 2 from the right on a graph.

Flashcard 29: Determine the limit if $\text{lim}_{x \to 0^-} f(x) = -4$ and $\text{lim}_{x \to 0^+} f(x) = 4$ .

Flashcard 30: If a graph has a vertical asymptote at $x = 1$ , what is $\text{lim}_{x \to 1} f(x)$ ?

Flashcard 31: Find $\text{lim}_{x \to 2} f(x)$ if the graph is continuous at $x = 2$ and $f(2) = 8$ .

Flashcard 32: What is $\text{lim}_{x \to \text{infinity}} f(x)$ if the graph levels off at 7?

Flashcard 33: What is $\text{lim}_{x \to 3} f(x)$ if the graph shows a hole at $x = 3$ ?

Flashcard 34: Estimate $\text{lim}_{x \to 0} f(x)$ from a graph with a vertical asymptote at $x = 0$ .

Flashcard 35: Estimate $\text{lim}_{x \to 2} f(x)$ from a graph where $f(x)$ approaches $-3$ .

Flashcard 36: Estimate $\text{lim}_{x \to 5} f(x)$ if graph approaches different values from left and right.

Flashcard 37: Which notation represents the limit of $f(x)$ as $x$ approaches 0 from the left?

Flashcard 38: Estimate $\text{lim}_{x \to -\text{infinity}} f(x)$ if the graph approaches 0.

Flashcard 39: Determine $\lim_{x \to 0} f(x)$ if graph shows $f(x)$ approaches 3 from both sides.

Flashcard 40: Estimate $\text{lim}_{x \to -2} f(x)$ from the graph if $f(x)$ approaches 5.

Flashcard 41: What is the implication if $\text{lim}_{x \to c} f(x)$ exists but $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Flashcard 42: Estimate $\text{lim}_{x \to 2} f(x)$ from a graph where $f(x)$ approaches $-3$ .

Flashcard 43: What is the implication if $\text{lim}_{x \to c} f(x)$ exists but $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Flashcard 44: Estimate $\text{lim}_{x \to 7} f(x)$ if the graph shows a removable discontinuity at $x = 7$ .

Flashcard 45: Estimate $\lim_{x \to 3^-} f(x)$ if the graph shows $f(x)$ approaching 6.

Flashcard 46: What is implied if $\text{lim}_{x \to \text{infinity}} f(x) = L$ ?

Flashcard 47: Find $\text{lim}_{x \to 2} f(x)$ if the graph is continuous at $x = 2$ and $f(2) = 8$ .

Flashcard 48: Estimate $\lim_{x \to \infty} f(x)$ from a graph that approaches $y = 0$ .

Flashcard 49: Identify $\text{lim}_{x \to 1^+} f(x)$ from a graph approaching value 4.

Flashcard 50: What does the graph of $f(x)$ show if $\text{lim}_{x \to c} f(x) \neq f(c)$ ?

Flashcard 51: Determine $\text{lim}_{x \to 0} f(x)$ if graph shows $f(x)$ approaches 3 from both sides.

Flashcard 52: Estimate $\text{lim}_{x \to 7} f(x)$ if the graph shows a removable discontinuity at $x = 7$ .

Flashcard 53: What is indicated by $\text{lim}_{x \to c} f(x) = L$ on a continuous graph?

Flashcard 54: Identify the limit of $f(x)$ as $x$ approaches 2 from the right on a graph.