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AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

Study Limits At Infinity And Horizontal Asymptotes in AP Calculus BC with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Limits At Infinity And Horizontal Asymptotes, 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.

AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

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QUESTION

What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Tap or drag to reveal answer

ANSWER

None. Numerator degree exceeds denominator degree.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 2: State the horizontal asymptote for $f(x) = \frac{x^3 - x}{3x^3 + 5}$ .

Answer: $y = \frac{1}{3}$ . Cubic leading coefficients: $\frac{1}{3}$ .

Flashcard 3: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 5}{4x^2 + 7}$ .

Answer: $y = \frac{3}{4}$ . Quadratic coefficients: $\frac{3}{4}$ .

Flashcard 4: Determine the horizontal asymptote of $f(x) = \frac{4x}{x^3 + 1}$ .

Answer: $y = 0$ . Numerator degree less than denominator degree.

Flashcard 5: Find the horizontal asymptote for $f(x) = \frac{2x^4 + 3x}{x^4 + x^2}$ .

Answer: $y = 2$ . Fourth-degree terms dominate: $\frac{2}{1} = 2$ .

Flashcard 6: Identify the horizontal asymptote of $f(x) = \frac{7x^3 + 5}{3x^3 - 2}$ .

Answer: $y = \frac{7}{3}$ . Equal degree cubic polynomials: $\frac{7}{3}$ .

Flashcard 7: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^3 + 7}$ ?

Answer: $y = \frac{5}{2}$ . Ratio of leading coefficients for equal-degree polynomials.

Flashcard 8: What is the horizontal asymptote of $f(x) = \frac{2x^2 - 5x}{5x^2 + x}$ ?

Answer: $y = \frac{2}{5}$ . Quadratic terms: $\frac{2}{5}$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 + 2}{2x^2 - 3}$ .

Answer: $y = \frac{1}{2}$ . Leading coefficient ratio: $\frac{1}{2}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{2x^3}{x^2 + x}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{x^3 + 2}{4x^3 + x}$ ?

Answer: $y = \frac{1}{4}$ . Cubic coefficients: $\frac{1}{4}$ .

Flashcard 12: State the horizontal asymptote for $f(x) = \frac{2x}{x^3 + 5}$ .

Answer: $y = 0$ . Linear over cubic approaches 0.

Flashcard 13: Find the horizontal asymptote for $f(x) = \frac{3x^4 - 2x}{2x^4 + 5}$ .

Answer: $y = \frac{3}{2}$ . Fourth-degree leading coefficients: $\frac{3}{2}$ .

Flashcard 14: What is the horizontal asymptote of $f(x) = \frac{5x}{x^2 + x}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 15: Find the horizontal asymptote for $f(x) = \frac{4x^2 - x}{x^2 + x}$ .

Answer: $y = 4$ . Quadratic coefficients: $\frac{4}{1} = 4$ .

Flashcard 16: What is the horizontal asymptote of $f(x) = \frac{x^2 + 7x}{3x^2 - 9}$ ?

Answer: $y = \frac{1}{3}$ . Quadratic leading coefficients: $\frac{1}{3}$ .

Flashcard 17: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 4x}{x^2}$ ?

Answer: $y = 2$ . Simplify to $\frac{2x^2 + 4x}{x^2} = 2 + \frac{4}{x}$ .

Flashcard 18: Determine the horizontal asymptote of $f(x) = \frac{7x^3}{3x^3 + 2x}$ .

Answer: $y = \frac{7}{3}$ . Cubic terms: $\frac{7}{3}$ .

Flashcard 19: Find the horizontal asymptote for $f(x) = \frac{x^3}{x^3 + x}$ .

Answer: $y = 1$ . Cubic terms: $\frac{1}{1} = 1$ .

Flashcard 20: What is the limit of $f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}$ as $x$ approaches infinity?

Answer: $4$ . Leading coefficient ratio when degrees match.

Flashcard 21: Identify the horizontal asymptote of $f(x) = \frac{x}{x^3 + 1}$ .

Answer: $y = 0$ . Linear over cubic approaches 0.

Flashcard 22: What is the horizontal asymptote of $f(x) = \frac{4x}{x^2 + 1}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 23: Identify the horizontal asymptote of $f(x) = \frac{x^2 + 3}{2x^2 - 1}$ .

Answer: $y = \frac{1}{2}$ . Quadratic coefficients: $\frac{1}{2}$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 + 5}{4x^4 + 1}$ ?

Answer: $y = 0$ . Numerator degree less than denominator degree.

Flashcard 25: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{x^2 - x}$ .

Answer: $y = 3$ . Quadratic terms: $\frac{3}{1} = 3$ .

Flashcard 26: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^2 + x}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 27: State the horizontal asymptote for $f(x) = \frac{x^2 - 4}{x^2 + 5}$ .

Answer: $y = 1$ . Equal-degree quadratics: $\frac{1}{1} = 1$ .

Flashcard 28: What is the limit of $f(x) = \frac{6x^3}{3x^4 + 2}$ as $x$ approaches infinity?

Answer: $0$ . Numerator degree less than denominator degree.

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{2x}{x^2 + 1}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 30: Find the horizontal asymptote for $f(x) = \frac{4x^3 + 1}{x^3 - 2}$ .

Answer: $y = 4$ . Cubic terms give $\frac{4}{1} = 4$ .

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AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

Study Limits At Infinity And Horizontal Asymptotes in AP Calculus BC 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 Limits At Infinity And Horizontal Asymptotes, 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.

AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Tap or drag to reveal answer

ANSWER

None. Numerator degree exceeds denominator degree.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 2: State the horizontal asymptote for $f(x) = \frac{x^3 - x}{3x^3 + 5}$ .

Answer: $y = \frac{1}{3}$ . Cubic leading coefficients: $\frac{1}{3}$ .

Flashcard 3: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 5}{4x^2 + 7}$ .

Answer: $y = \frac{3}{4}$ . Quadratic coefficients: $\frac{3}{4}$ .

Flashcard 4: Determine the horizontal asymptote of $f(x) = \frac{4x}{x^3 + 1}$ .

Answer: $y = 0$ . Numerator degree less than denominator degree.

Flashcard 5: Find the horizontal asymptote for $f(x) = \frac{2x^4 + 3x}{x^4 + x^2}$ .

Answer: $y = 2$ . Fourth-degree terms dominate: $\frac{2}{1} = 2$ .

Flashcard 6: Identify the horizontal asymptote of $f(x) = \frac{7x^3 + 5}{3x^3 - 2}$ .

Answer: $y = \frac{7}{3}$ . Equal degree cubic polynomials: $\frac{7}{3}$ .

Flashcard 7: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^3 + 7}$ ?

Answer: $y = \frac{5}{2}$ . Ratio of leading coefficients for equal-degree polynomials.

Flashcard 8: What is the horizontal asymptote of $f(x) = \frac{2x^2 - 5x}{5x^2 + x}$ ?

Answer: $y = \frac{2}{5}$ . Quadratic terms: $\frac{2}{5}$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 + 2}{2x^2 - 3}$ .

Answer: $y = \frac{1}{2}$ . Leading coefficient ratio: $\frac{1}{2}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{2x^3}{x^2 + x}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{x^3 + 2}{4x^3 + x}$ ?

Answer: $y = \frac{1}{4}$ . Cubic coefficients: $\frac{1}{4}$ .

Flashcard 12: State the horizontal asymptote for $f(x) = \frac{2x}{x^3 + 5}$ .

Answer: $y = 0$ . Linear over cubic approaches 0.

Flashcard 13: Find the horizontal asymptote for $f(x) = \frac{3x^4 - 2x}{2x^4 + 5}$ .

Answer: $y = \frac{3}{2}$ . Fourth-degree leading coefficients: $\frac{3}{2}$ .

Flashcard 14: What is the horizontal asymptote of $f(x) = \frac{5x}{x^2 + x}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 15: Find the horizontal asymptote for $f(x) = \frac{4x^2 - x}{x^2 + x}$ .

Answer: $y = 4$ . Quadratic coefficients: $\frac{4}{1} = 4$ .

Flashcard 16: What is the horizontal asymptote of $f(x) = \frac{x^2 + 7x}{3x^2 - 9}$ ?

Answer: $y = \frac{1}{3}$ . Quadratic leading coefficients: $\frac{1}{3}$ .

Flashcard 17: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 4x}{x^2}$ ?

Answer: $y = 2$ . Simplify to $\frac{2x^2 + 4x}{x^2} = 2 + \frac{4}{x}$ .

Flashcard 18: Determine the horizontal asymptote of $f(x) = \frac{7x^3}{3x^3 + 2x}$ .

Answer: $y = \frac{7}{3}$ . Cubic terms: $\frac{7}{3}$ .

Flashcard 19: Find the horizontal asymptote for $f(x) = \frac{x^3}{x^3 + x}$ .

Answer: $y = 1$ . Cubic terms: $\frac{1}{1} = 1$ .

Flashcard 20: What is the limit of $f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}$ as $x$ approaches infinity?

Answer: $4$ . Leading coefficient ratio when degrees match.

Flashcard 21: Identify the horizontal asymptote of $f(x) = \frac{x}{x^3 + 1}$ .

Answer: $y = 0$ . Linear over cubic approaches 0.

Flashcard 22: What is the horizontal asymptote of $f(x) = \frac{4x}{x^2 + 1}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 23: Identify the horizontal asymptote of $f(x) = \frac{x^2 + 3}{2x^2 - 1}$ .

Answer: $y = \frac{1}{2}$ . Quadratic coefficients: $\frac{1}{2}$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 + 5}{4x^4 + 1}$ ?

Answer: $y = 0$ . Numerator degree less than denominator degree.

Flashcard 25: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{x^2 - x}$ .

Answer: $y = 3$ . Quadratic terms: $\frac{3}{1} = 3$ .

Flashcard 26: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^2 + x}$ ?

Answer: None. Numerator degree exceeds denominator degree.

Flashcard 27: State the horizontal asymptote for $f(x) = \frac{x^2 - 4}{x^2 + 5}$ .

Answer: $y = 1$ . Equal-degree quadratics: $\frac{1}{1} = 1$ .

Flashcard 28: What is the limit of $f(x) = \frac{6x^3}{3x^4 + 2}$ as $x$ approaches infinity?

Answer: $0$ . Numerator degree less than denominator degree.

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{2x}{x^2 + 1}$ ?

Answer: $y = 0$ . Linear over quadratic approaches 0.

Flashcard 30: Find the horizontal asymptote for $f(x) = \frac{4x^3 + 1}{x^3 - 2}$ .

Answer: $y = 4$ . Cubic terms give $\frac{4}{1} = 4$ .

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AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

What this deck covers

How to use these flashcards

AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

All flashcards

Flashcard 1: What is the horizontal asymptote of f(x)=4x4x3+2f(x) = \frac{4x^4}{x^3 + 2}f(x)=x3+24x4​?

Flashcard 2: State the horizontal asymptote for f(x)=x3−x3x3+5f(x) = \frac{x^3 - x}{3x^3 + 5}f(x)=3x3+5x3−x​.

Flashcard 3: Determine the horizontal asymptote of f(x)=3x2+54x2+7f(x) = \frac{3x^2 + 5}{4x^2 + 7}f(x)=4x2+73x2+5​.

Flashcard 4: Determine the horizontal asymptote of f(x)=4xx3+1f(x) = \frac{4x}{x^3 + 1}f(x)=x3+14x​.

Flashcard 5: Find the horizontal asymptote for f(x)=2x4+3xx4+x2f(x) = \frac{2x^4 + 3x}{x^4 + x^2}f(x)=x4+x22x4+3x​.

Flashcard 6: Identify the horizontal asymptote of f(x)=7x3+53x3−2f(x) = \frac{7x^3 + 5}{3x^3 - 2}f(x)=3x3−27x3+5​.

Flashcard 7: What is the horizontal asymptote of f(x)=5x32x3+7f(x) = \frac{5x^3}{2x^3 + 7}f(x)=2x3+75x3​?

Flashcard 8: What is the horizontal asymptote of f(x)=2x2−5x5x2+xf(x) = \frac{2x^2 - 5x}{5x^2 + x}f(x)=5x2+x2x2−5x​?

Flashcard 9: State the horizontal asymptote of f(x)=x2+22x2−3f(x) = \frac{x^2 + 2}{2x^2 - 3}f(x)=2x2−3x2+2​.

Flashcard 10: What is the horizontal asymptote of f(x)=2x3x2+xf(x) = \frac{2x^3}{x^2 + x}f(x)=x2+x2x3​?

Flashcard 11: What is the horizontal asymptote of f(x)=x3+24x3+xf(x) = \frac{x^3 + 2}{4x^3 + x}f(x)=4x3+xx3+2​?

Flashcard 12: State the horizontal asymptote for f(x)=2xx3+5f(x) = \frac{2x}{x^3 + 5}f(x)=x3+52x​.

Flashcard 13: Find the horizontal asymptote for f(x)=3x4−2x2x4+5f(x) = \frac{3x^4 - 2x}{2x^4 + 5}f(x)=2x4+53x4−2x​.

Flashcard 14: What is the horizontal asymptote of f(x)=5xx2+xf(x) = \frac{5x}{x^2 + x}f(x)=x2+x5x​?

Flashcard 15: Find the horizontal asymptote for f(x)=4x2−xx2+xf(x) = \frac{4x^2 - x}{x^2 + x}f(x)=x2+x4x2−x​.

Flashcard 16: What is the horizontal asymptote of f(x)=x2+7x3x2−9f(x) = \frac{x^2 + 7x}{3x^2 - 9}f(x)=3x2−9x2+7x​?

Flashcard 17: What is the horizontal asymptote of f(x)=2x2+4xx2f(x) = \frac{2x^2 + 4x}{x^2}f(x)=x22x2+4x​?

Flashcard 18: Determine the horizontal asymptote of f(x)=7x33x3+2xf(x) = \frac{7x^3}{3x^3 + 2x}f(x)=3x3+2x7x3​.

Flashcard 19: Find the horizontal asymptote for f(x)=x3x3+xf(x) = \frac{x^3}{x^3 + x}f(x)=x3+xx3​.

Flashcard 20: What is the limit of f(x)=4x2−x+6x2+x−12f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}f(x)=x2+x−124x2−x+6​ as xxx approaches infinity?

Flashcard 21: Identify the horizontal asymptote of f(x)=xx3+1f(x) = \frac{x}{x^3 + 1}f(x)=x3+1x​.

Flashcard 22: What is the horizontal asymptote of f(x)=4xx2+1f(x) = \frac{4x}{x^2 + 1}f(x)=x2+14x​?

Flashcard 23: Identify the horizontal asymptote of f(x)=x2+32x2−1f(x) = \frac{x^2 + 3}{2x^2 - 1}f(x)=2x2−1x2+3​.

Flashcard 24: What is the horizontal asymptote of f(x)=x3+54x4+1f(x) = \frac{x^3 + 5}{4x^4 + 1}f(x)=4x4+1x3+5​?

Flashcard 25: Determine the horizontal asymptote of f(x)=3x2+2x2−xf(x) = \frac{3x^2 + 2}{x^2 - x}f(x)=x2−x3x2+2​.

Flashcard 26: What is the horizontal asymptote of f(x)=5x32x2+xf(x) = \frac{5x^3}{2x^2 + x}f(x)=2x2+x5x3​?

Flashcard 27: State the horizontal asymptote for f(x)=x2−4x2+5f(x) = \frac{x^2 - 4}{x^2 + 5}f(x)=x2+5x2−4​.

Flashcard 28: What is the limit of f(x)=6x33x4+2f(x) = \frac{6x^3}{3x^4 + 2}f(x)=3x4+26x3​ as xxx approaches infinity?

Flashcard 29: What is the horizontal asymptote of f(x)=2xx2+1f(x) = \frac{2x}{x^2 + 1}f(x)=x2+12x​?

Flashcard 30: Find the horizontal asymptote for f(x)=4x3+1x3−2f(x) = \frac{4x^3 + 1}{x^3 - 2}f(x)=x3−24x3+1​.

Opening subject page...

AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

What this deck covers

How to use these flashcards

AP Calculus BC Flashcards: Limits At Infinity And Horizontal Asymptotes

All flashcards

Flashcard 1: What is the horizontal asymptote of f(x)=4x4x3+2f(x) = \frac{4x^4}{x^3 + 2}f(x)=x3+24x4​?

Flashcard 2: State the horizontal asymptote for f(x)=x3−x3x3+5f(x) = \frac{x^3 - x}{3x^3 + 5}f(x)=3x3+5x3−x​.

Flashcard 3: Determine the horizontal asymptote of f(x)=3x2+54x2+7f(x) = \frac{3x^2 + 5}{4x^2 + 7}f(x)=4x2+73x2+5​.

Flashcard 4: Determine the horizontal asymptote of f(x)=4xx3+1f(x) = \frac{4x}{x^3 + 1}f(x)=x3+14x​.

Flashcard 5: Find the horizontal asymptote for f(x)=2x4+3xx4+x2f(x) = \frac{2x^4 + 3x}{x^4 + x^2}f(x)=x4+x22x4+3x​.

Flashcard 6: Identify the horizontal asymptote of f(x)=7x3+53x3−2f(x) = \frac{7x^3 + 5}{3x^3 - 2}f(x)=3x3−27x3+5​.

Flashcard 7: What is the horizontal asymptote of f(x)=5x32x3+7f(x) = \frac{5x^3}{2x^3 + 7}f(x)=2x3+75x3​?

Flashcard 8: What is the horizontal asymptote of f(x)=2x2−5x5x2+xf(x) = \frac{2x^2 - 5x}{5x^2 + x}f(x)=5x2+x2x2−5x​?

Flashcard 9: State the horizontal asymptote of f(x)=x2+22x2−3f(x) = \frac{x^2 + 2}{2x^2 - 3}f(x)=2x2−3x2+2​.

Flashcard 10: What is the horizontal asymptote of f(x)=2x3x2+xf(x) = \frac{2x^3}{x^2 + x}f(x)=x2+x2x3​?

Flashcard 11: What is the horizontal asymptote of f(x)=x3+24x3+xf(x) = \frac{x^3 + 2}{4x^3 + x}f(x)=4x3+xx3+2​?

Flashcard 12: State the horizontal asymptote for f(x)=2xx3+5f(x) = \frac{2x}{x^3 + 5}f(x)=x3+52x​.

Flashcard 13: Find the horizontal asymptote for f(x)=3x4−2x2x4+5f(x) = \frac{3x^4 - 2x}{2x^4 + 5}f(x)=2x4+53x4−2x​.

Flashcard 14: What is the horizontal asymptote of f(x)=5xx2+xf(x) = \frac{5x}{x^2 + x}f(x)=x2+x5x​?

Flashcard 15: Find the horizontal asymptote for f(x)=4x2−xx2+xf(x) = \frac{4x^2 - x}{x^2 + x}f(x)=x2+x4x2−x​.

Flashcard 16: What is the horizontal asymptote of f(x)=x2+7x3x2−9f(x) = \frac{x^2 + 7x}{3x^2 - 9}f(x)=3x2−9x2+7x​?

Flashcard 17: What is the horizontal asymptote of f(x)=2x2+4xx2f(x) = \frac{2x^2 + 4x}{x^2}f(x)=x22x2+4x​?

Flashcard 18: Determine the horizontal asymptote of f(x)=7x33x3+2xf(x) = \frac{7x^3}{3x^3 + 2x}f(x)=3x3+2x7x3​.

Flashcard 19: Find the horizontal asymptote for f(x)=x3x3+xf(x) = \frac{x^3}{x^3 + x}f(x)=x3+xx3​.

Flashcard 20: What is the limit of f(x)=4x2−x+6x2+x−12f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}f(x)=x2+x−124x2−x+6​ as xxx approaches infinity?

Flashcard 21: Identify the horizontal asymptote of f(x)=xx3+1f(x) = \frac{x}{x^3 + 1}f(x)=x3+1x​.

Flashcard 22: What is the horizontal asymptote of f(x)=4xx2+1f(x) = \frac{4x}{x^2 + 1}f(x)=x2+14x​?

Flashcard 23: Identify the horizontal asymptote of f(x)=x2+32x2−1f(x) = \frac{x^2 + 3}{2x^2 - 1}f(x)=2x2−1x2+3​.

Flashcard 24: What is the horizontal asymptote of f(x)=x3+54x4+1f(x) = \frac{x^3 + 5}{4x^4 + 1}f(x)=4x4+1x3+5​?

Flashcard 25: Determine the horizontal asymptote of f(x)=3x2+2x2−xf(x) = \frac{3x^2 + 2}{x^2 - x}f(x)=x2−x3x2+2​.

Flashcard 26: What is the horizontal asymptote of f(x)=5x32x2+xf(x) = \frac{5x^3}{2x^2 + x}f(x)=2x2+x5x3​?

Flashcard 27: State the horizontal asymptote for f(x)=x2−4x2+5f(x) = \frac{x^2 - 4}{x^2 + 5}f(x)=x2+5x2−4​.

Flashcard 28: What is the limit of f(x)=6x33x4+2f(x) = \frac{6x^3}{3x^4 + 2}f(x)=3x4+26x3​ as xxx approaches infinity?

Flashcard 29: What is the horizontal asymptote of f(x)=2xx2+1f(x) = \frac{2x}{x^2 + 1}f(x)=x2+12x​?

Flashcard 30: Find the horizontal asymptote for f(x)=4x3+1x3−2f(x) = \frac{4x^3 + 1}{x^3 - 2}f(x)=x3−24x3+1​.

Flashcard 1: What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Flashcard 2: State the horizontal asymptote for $f(x) = \frac{x^3 - x}{3x^3 + 5}$ .

Flashcard 3: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 5}{4x^2 + 7}$ .

Flashcard 4: Determine the horizontal asymptote of $f(x) = \frac{4x}{x^3 + 1}$ .

Flashcard 5: Find the horizontal asymptote for $f(x) = \frac{2x^4 + 3x}{x^4 + x^2}$ .

Flashcard 6: Identify the horizontal asymptote of $f(x) = \frac{7x^3 + 5}{3x^3 - 2}$ .

Flashcard 7: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^3 + 7}$ ?

Flashcard 8: What is the horizontal asymptote of $f(x) = \frac{2x^2 - 5x}{5x^2 + x}$ ?

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 + 2}{2x^2 - 3}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{2x^3}{x^2 + x}$ ?

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{x^3 + 2}{4x^3 + x}$ ?

Flashcard 12: State the horizontal asymptote for $f(x) = \frac{2x}{x^3 + 5}$ .

Flashcard 13: Find the horizontal asymptote for $f(x) = \frac{3x^4 - 2x}{2x^4 + 5}$ .

Flashcard 14: What is the horizontal asymptote of $f(x) = \frac{5x}{x^2 + x}$ ?

Flashcard 15: Find the horizontal asymptote for $f(x) = \frac{4x^2 - x}{x^2 + x}$ .

Flashcard 16: What is the horizontal asymptote of $f(x) = \frac{x^2 + 7x}{3x^2 - 9}$ ?

Flashcard 17: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 4x}{x^2}$ ?

Flashcard 18: Determine the horizontal asymptote of $f(x) = \frac{7x^3}{3x^3 + 2x}$ .

Flashcard 19: Find the horizontal asymptote for $f(x) = \frac{x^3}{x^3 + x}$ .

Flashcard 20: What is the limit of $f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}$ as $x$ approaches infinity?

Flashcard 21: Identify the horizontal asymptote of $f(x) = \frac{x}{x^3 + 1}$ .

Flashcard 22: What is the horizontal asymptote of $f(x) = \frac{4x}{x^2 + 1}$ ?

Flashcard 23: Identify the horizontal asymptote of $f(x) = \frac{x^2 + 3}{2x^2 - 1}$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 + 5}{4x^4 + 1}$ ?

Flashcard 25: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{x^2 - x}$ .

Flashcard 26: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^2 + x}$ ?

Flashcard 27: State the horizontal asymptote for $f(x) = \frac{x^2 - 4}{x^2 + 5}$ .

Flashcard 28: What is the limit of $f(x) = \frac{6x^3}{3x^4 + 2}$ as $x$ approaches infinity?

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{2x}{x^2 + 1}$ ?

Flashcard 30: Find the horizontal asymptote for $f(x) = \frac{4x^3 + 1}{x^3 - 2}$ .

Flashcard 1: What is the horizontal asymptote of $f(x) = \frac{4x^4}{x^3 + 2}$ ?

Flashcard 2: State the horizontal asymptote for $f(x) = \frac{x^3 - x}{3x^3 + 5}$ .

Flashcard 3: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 5}{4x^2 + 7}$ .

Flashcard 4: Determine the horizontal asymptote of $f(x) = \frac{4x}{x^3 + 1}$ .

Flashcard 5: Find the horizontal asymptote for $f(x) = \frac{2x^4 + 3x}{x^4 + x^2}$ .

Flashcard 6: Identify the horizontal asymptote of $f(x) = \frac{7x^3 + 5}{3x^3 - 2}$ .

Flashcard 7: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^3 + 7}$ ?

Flashcard 8: What is the horizontal asymptote of $f(x) = \frac{2x^2 - 5x}{5x^2 + x}$ ?

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 + 2}{2x^2 - 3}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{2x^3}{x^2 + x}$ ?

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{x^3 + 2}{4x^3 + x}$ ?

Flashcard 12: State the horizontal asymptote for $f(x) = \frac{2x}{x^3 + 5}$ .

Flashcard 13: Find the horizontal asymptote for $f(x) = \frac{3x^4 - 2x}{2x^4 + 5}$ .

Flashcard 14: What is the horizontal asymptote of $f(x) = \frac{5x}{x^2 + x}$ ?

Flashcard 15: Find the horizontal asymptote for $f(x) = \frac{4x^2 - x}{x^2 + x}$ .

Flashcard 16: What is the horizontal asymptote of $f(x) = \frac{x^2 + 7x}{3x^2 - 9}$ ?

Flashcard 17: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 4x}{x^2}$ ?

Flashcard 18: Determine the horizontal asymptote of $f(x) = \frac{7x^3}{3x^3 + 2x}$ .

Flashcard 19: Find the horizontal asymptote for $f(x) = \frac{x^3}{x^3 + x}$ .

Flashcard 20: What is the limit of $f(x) = \frac{4x^2 - x + 6}{x^2 + x - 12}$ as $x$ approaches infinity?

Flashcard 21: Identify the horizontal asymptote of $f(x) = \frac{x}{x^3 + 1}$ .

Flashcard 22: What is the horizontal asymptote of $f(x) = \frac{4x}{x^2 + 1}$ ?

Flashcard 23: Identify the horizontal asymptote of $f(x) = \frac{x^2 + 3}{2x^2 - 1}$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 + 5}{4x^4 + 1}$ ?

Flashcard 25: Determine the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{x^2 - x}$ .

Flashcard 26: What is the horizontal asymptote of $f(x) = \frac{5x^3}{2x^2 + x}$ ?

Flashcard 27: State the horizontal asymptote for $f(x) = \frac{x^2 - 4}{x^2 + 5}$ .

Flashcard 28: What is the limit of $f(x) = \frac{6x^3}{3x^4 + 2}$ as $x$ approaches infinity?

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{2x}{x^2 + 1}$ ?

Flashcard 30: Find the horizontal asymptote for $f(x) = \frac{4x^3 + 1}{x^3 - 2}$ .