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AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

Study Limits At Infinity And Horizontal Asymptotes in AP Calculus AB 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 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: Limits At Infinity And Horizontal Asymptotes

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QUESTION

Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Tap or drag to reveal answer

ANSWER

$\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Answer: $\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

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

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 3: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Answer: $y = 4$ . Same degree; ratio of leading coefficients is $\frac{4}{1} = 4$ .

Flashcard 4: Determine $\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}$ .

Answer: $\frac{2}{3}$ . Same degree; ratio of leading coefficients is $\frac{2}{3}$ .

Flashcard 5: Find the horizontal asymptote of $f(x) = \frac{x + 1}{x^2 + 1}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so horizontal asymptote is $y = 0$ .

Flashcard 6: State the horizontal asymptote of $f(x) = \frac{8x}{x^2 + 3}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 7: Find the limit as $x$ approaches infinity for $f(x) = \frac{7x^3}{2x^3 + 5}$ .

Answer: $\frac{7}{2}$ . Same degree; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 8: Find the horizontal asymptote of $f(x) = \frac{6x^3}{3x^3 + 1}$ .

Answer: $y = 2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 - 3}{2x^2 + x + 1}$ .

Answer: $y = \frac{1}{2}$ . Same degree; ratio of leading coefficients is $\frac{1}{2}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{8x^3 + 1}{4x^3 + 2}$ ?

Answer: $y = 2$ . Same degree; ratio of leading coefficients is $\frac{8}{4} = 2$ .

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 3}{x^2 + 5}$ ?

Answer: $y = 2$ . Same degree numerator and denominator; ratio of leading coefficients is $\frac{2}{1} = 2$ .

Flashcard 12: What is the horizontal asymptote of $f(x) = \frac{3x + 2}{2x^2 + 5}$ ?

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 13: What is the limit as $x$ approaches infinity for $f(x) = \frac{3x^3 + 2}{x^2 + 4}$ ?

Answer: Infinity. Numerator degree exceeds denominator degree, so limit approaches infinity.

Flashcard 14: Determine $\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}$ .

Answer: $\frac{-1}{3}$ . Same degree; ratio of leading coefficients is $\frac{-1}{3}$ .

Flashcard 15: Find the limit as $x$ approaches infinity of $f(x) = \frac{3x^4}{x^4 + 5}$ .

Answer: $3$ . Same degree; ratio of leading coefficients is $\frac{3}{1} = 3$ .

Flashcard 16: Determine $\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}$ .

Answer: $4$ . Same degree; ratio of leading coefficients is $\frac{8}{2} = 4$ .

Flashcard 17: State the horizontal asymptote of $f(x) = \frac{7x^2 - x}{3x^2 + 2}$ .

Answer: $y = \frac{7}{3}$ . Same degree; ratio of leading coefficients is $\frac{7}{3}$ .

Flashcard 18: Find the horizontal asymptote of $f(x) = \frac{5x^3 - 2x}{4x^3 + x}$ .

Answer: $y = \frac{5}{4}$ . Same degree; ratio of leading coefficients is $\frac{5}{4}$ .

Flashcard 19: Determine $\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}$ .

Answer: $1$ . Same degree; ratio of leading coefficients is $\frac{1}{1} = 1$ .

Flashcard 20: What is the horizontal asymptote for $f(x) = \frac{2x^3}{5x^3 - 4}$ ?

Answer: $y = \frac{2}{5}$ . Same degree; ratio of leading coefficients is $\frac{2}{5}$ .

Flashcard 21: Determine $\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}$ .

Answer: $\frac{7}{2}$ . Same degree; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 22: State the horizontal asymptote of $f(x) = \frac{x^2 + x}{x^3 + 1}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 23: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 - 1}{x^2 + 3x}$ ?

Answer: None. Numerator degree exceeds denominator degree, so no horizontal asymptote exists.

Flashcard 25: Find the limit as $x$ approaches infinity of $f(x) = \frac{4x^2}{2x^2 + 3}$ .

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{4}{2} = 2$ .

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

Answer: $y = \frac{5}{3}$ . Same degree; ratio of leading coefficients is $\frac{5}{3}$ .

Flashcard 27: What is the horizontal asymptote of $f(x) = \frac{7x}{2x + 3}$ ?

Answer: $y = \frac{7}{2}$ . Same degree polynomials; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 28: Determine $\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Answer: $\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Answer: $y = 4$ . Same degree; ratio of leading coefficients is $\frac{4}{1} = 4$ .

Flashcard 30: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

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AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

Study Limits At Infinity And Horizontal Asymptotes 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 Limits At Infinity And Horizontal Asymptotes, 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: Limits At Infinity And Horizontal Asymptotes

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Tap or drag to reveal answer

ANSWER

$\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Answer: $\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

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

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 3: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Answer: $y = 4$ . Same degree; ratio of leading coefficients is $\frac{4}{1} = 4$ .

Flashcard 4: Determine $\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}$ .

Answer: $\frac{2}{3}$ . Same degree; ratio of leading coefficients is $\frac{2}{3}$ .

Flashcard 5: Find the horizontal asymptote of $f(x) = \frac{x + 1}{x^2 + 1}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so horizontal asymptote is $y = 0$ .

Flashcard 6: State the horizontal asymptote of $f(x) = \frac{8x}{x^2 + 3}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 7: Find the limit as $x$ approaches infinity for $f(x) = \frac{7x^3}{2x^3 + 5}$ .

Answer: $\frac{7}{2}$ . Same degree; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 8: Find the horizontal asymptote of $f(x) = \frac{6x^3}{3x^3 + 1}$ .

Answer: $y = 2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 - 3}{2x^2 + x + 1}$ .

Answer: $y = \frac{1}{2}$ . Same degree; ratio of leading coefficients is $\frac{1}{2}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{8x^3 + 1}{4x^3 + 2}$ ?

Answer: $y = 2$ . Same degree; ratio of leading coefficients is $\frac{8}{4} = 2$ .

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 3}{x^2 + 5}$ ?

Answer: $y = 2$ . Same degree numerator and denominator; ratio of leading coefficients is $\frac{2}{1} = 2$ .

Flashcard 12: What is the horizontal asymptote of $f(x) = \frac{3x + 2}{2x^2 + 5}$ ?

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 13: What is the limit as $x$ approaches infinity for $f(x) = \frac{3x^3 + 2}{x^2 + 4}$ ?

Answer: Infinity. Numerator degree exceeds denominator degree, so limit approaches infinity.

Flashcard 14: Determine $\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}$ .

Answer: $\frac{-1}{3}$ . Same degree; ratio of leading coefficients is $\frac{-1}{3}$ .

Flashcard 15: Find the limit as $x$ approaches infinity of $f(x) = \frac{3x^4}{x^4 + 5}$ .

Answer: $3$ . Same degree; ratio of leading coefficients is $\frac{3}{1} = 3$ .

Flashcard 16: Determine $\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}$ .

Answer: $4$ . Same degree; ratio of leading coefficients is $\frac{8}{2} = 4$ .

Flashcard 17: State the horizontal asymptote of $f(x) = \frac{7x^2 - x}{3x^2 + 2}$ .

Answer: $y = \frac{7}{3}$ . Same degree; ratio of leading coefficients is $\frac{7}{3}$ .

Flashcard 18: Find the horizontal asymptote of $f(x) = \frac{5x^3 - 2x}{4x^3 + x}$ .

Answer: $y = \frac{5}{4}$ . Same degree; ratio of leading coefficients is $\frac{5}{4}$ .

Flashcard 19: Determine $\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}$ .

Answer: $1$ . Same degree; ratio of leading coefficients is $\frac{1}{1} = 1$ .

Flashcard 20: What is the horizontal asymptote for $f(x) = \frac{2x^3}{5x^3 - 4}$ ?

Answer: $y = \frac{2}{5}$ . Same degree; ratio of leading coefficients is $\frac{2}{5}$ .

Flashcard 21: Determine $\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}$ .

Answer: $\frac{7}{2}$ . Same degree; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 22: State the horizontal asymptote of $f(x) = \frac{x^2 + x}{x^3 + 1}$ .

Answer: $y = 0$ . Denominator degree exceeds numerator degree, so asymptote is $y = 0$ .

Flashcard 23: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 - 1}{x^2 + 3x}$ ?

Answer: None. Numerator degree exceeds denominator degree, so no horizontal asymptote exists.

Flashcard 25: Find the limit as $x$ approaches infinity of $f(x) = \frac{4x^2}{2x^2 + 3}$ .

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{4}{2} = 2$ .

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

Answer: $y = \frac{5}{3}$ . Same degree; ratio of leading coefficients is $\frac{5}{3}$ .

Flashcard 27: What is the horizontal asymptote of $f(x) = \frac{7x}{2x + 3}$ ?

Answer: $y = \frac{7}{2}$ . Same degree polynomials; ratio of leading coefficients is $\frac{7}{2}$ .

Flashcard 28: Determine $\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Answer: $\frac{5}{2}$ . Divide by highest power; $\frac{5}{2}$ is the ratio of leading coefficients.

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Answer: $y = 4$ . Same degree; ratio of leading coefficients is $\frac{4}{1} = 4$ .

Flashcard 30: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Answer: $2$ . Same degree; ratio of leading coefficients is $\frac{6}{3} = 2$ .

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AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

All flashcards

Flashcard 1: Determine lim⁡x→∞5x−12x+3\lim_{x \to \infty} \frac{5x - 1}{2x + 3}limx→∞​2x+35x−1​.

Flashcard 2: What is the horizontal asymptote of f(x)=x2x3+1f(x) = \frac{x^2}{x^3 + 1}f(x)=x3+1x2​?

Flashcard 3: What is the horizontal asymptote of f(x)=4x3+5x3+6f(x) = \frac{4x^3 + 5}{x^3 + 6}f(x)=x3+64x3+5​?

Flashcard 4: Determine limx→∞2x3−53x3+1\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}limx→∞​3x3+12x3−5​.

Flashcard 5: Find the horizontal asymptote of f(x)=x+1x2+1f(x) = \frac{x + 1}{x^2 + 1}f(x)=x2+1x+1​.

Flashcard 6: State the horizontal asymptote of f(x)=8xx2+3f(x) = \frac{8x}{x^2 + 3}f(x)=x2+38x​.

Flashcard 7: Find the limit as xxx approaches infinity for f(x)=7x32x3+5f(x) = \frac{7x^3}{2x^3 + 5}f(x)=2x3+57x3​.

Flashcard 8: Find the horizontal asymptote of f(x)=6x33x3+1f(x) = \frac{6x^3}{3x^3 + 1}f(x)=3x3+16x3​.

Flashcard 9: State the horizontal asymptote of f(x)=x2−32x2+x+1f(x) = \frac{x^2 - 3}{2x^2 + x + 1}f(x)=2x2+x+1x2−3​.

Flashcard 10: What is the horizontal asymptote of f(x)=8x3+14x3+2f(x) = \frac{8x^3 + 1}{4x^3 + 2}f(x)=4x3+28x3+1​?

Flashcard 11: What is the horizontal asymptote of f(x)=2x2+3x2+5f(x) = \frac{2x^2 + 3}{x^2 + 5}f(x)=x2+52x2+3​?

Flashcard 12: What is the horizontal asymptote of f(x)=3x+22x2+5f(x) = \frac{3x + 2}{2x^2 + 5}f(x)=2x2+53x+2​?

Flashcard 13: What is the limit as xxx approaches infinity for f(x)=3x3+2x2+4f(x) = \frac{3x^3 + 2}{x^2 + 4}f(x)=x2+43x3+2​?

Flashcard 14: Determine limx→−∞−x3+43x3−x\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}limx→−∞​3x3−x−x3+4​.

Flashcard 15: Find the limit as xxx approaches infinity of f(x)=3x4x4+5f(x) = \frac{3x^4}{x^4 + 5}f(x)=x4+53x4​.

Flashcard 16: Determine limx→∞8x−32x+1\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}limx→∞​2x+18x−3​.

Flashcard 17: State the horizontal asymptote of f(x)=7x2−x3x2+2f(x) = \frac{7x^2 - x}{3x^2 + 2}f(x)=3x2+27x2−x​.

Flashcard 18: Find the horizontal asymptote of f(x)=5x3−2x4x3+xf(x) = \frac{5x^3 - 2x}{4x^3 + x}f(x)=4x3+x5x3−2x​.

Flashcard 19: Determine limx→−∞x2−2xx2+x\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}limx→−∞​x2+xx2−2x​.

Flashcard 20: What is the horizontal asymptote for f(x)=2x35x3−4f(x) = \frac{2x^3}{5x^3 - 4}f(x)=5x3−42x3​?

Flashcard 21: Determine limx→∞7x2−52x2+4\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}limx→∞​2x2+47x2−5​.

Flashcard 22: State the horizontal asymptote of f(x)=x2+xx3+1f(x) = \frac{x^2 + x}{x^3 + 1}f(x)=x3+1x2+x​.

Flashcard 23: What is the limit as xxx approaches infinity for f(x)=6x2−93x2+7f(x) = \frac{6x^2 - 9}{3x^2 + 7}f(x)=3x2+76x2−9​?

Flashcard 24: What is the horizontal asymptote of f(x)=x3−1x2+3xf(x) = \frac{x^3 - 1}{x^2 + 3x}f(x)=x2+3xx3−1​?

Flashcard 25: Find the limit as xxx approaches infinity of f(x)=4x22x2+3f(x) = \frac{4x^2}{2x^2 + 3}f(x)=2x2+34x2​.

Flashcard 26: State the horizontal asymptote of f(x)=5x23x2+2f(x) = \frac{5x^2}{3x^2 + 2}f(x)=3x2+25x2​.

Flashcard 27: What is the horizontal asymptote of f(x)=7x2x+3f(x) = \frac{7x}{2x + 3}f(x)=2x+37x​?

Flashcard 28: Determine limx→∞5x−12x+3\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}limx→∞​2x+35x−1​.

Flashcard 29: What is the horizontal asymptote of f(x)=4x3+5x3+6f(x) = \frac{4x^3 + 5}{x^3 + 6}f(x)=x3+64x3+5​?

Flashcard 30: What is the limit as xxx approaches infinity for f(x)=6x2−93x2+7f(x) = \frac{6x^2 - 9}{3x^2 + 7}f(x)=3x2+76x2−9​?

Opening subject page...

AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Limits At Infinity And Horizontal Asymptotes

All flashcards

Flashcard 1: Determine lim⁡x→∞5x−12x+3\lim_{x \to \infty} \frac{5x - 1}{2x + 3}limx→∞​2x+35x−1​.

Flashcard 2: What is the horizontal asymptote of f(x)=x2x3+1f(x) = \frac{x^2}{x^3 + 1}f(x)=x3+1x2​?

Flashcard 3: What is the horizontal asymptote of f(x)=4x3+5x3+6f(x) = \frac{4x^3 + 5}{x^3 + 6}f(x)=x3+64x3+5​?

Flashcard 4: Determine limx→∞2x3−53x3+1\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}limx→∞​3x3+12x3−5​.

Flashcard 5: Find the horizontal asymptote of f(x)=x+1x2+1f(x) = \frac{x + 1}{x^2 + 1}f(x)=x2+1x+1​.

Flashcard 6: State the horizontal asymptote of f(x)=8xx2+3f(x) = \frac{8x}{x^2 + 3}f(x)=x2+38x​.

Flashcard 7: Find the limit as xxx approaches infinity for f(x)=7x32x3+5f(x) = \frac{7x^3}{2x^3 + 5}f(x)=2x3+57x3​.

Flashcard 8: Find the horizontal asymptote of f(x)=6x33x3+1f(x) = \frac{6x^3}{3x^3 + 1}f(x)=3x3+16x3​.

Flashcard 9: State the horizontal asymptote of f(x)=x2−32x2+x+1f(x) = \frac{x^2 - 3}{2x^2 + x + 1}f(x)=2x2+x+1x2−3​.

Flashcard 10: What is the horizontal asymptote of f(x)=8x3+14x3+2f(x) = \frac{8x^3 + 1}{4x^3 + 2}f(x)=4x3+28x3+1​?

Flashcard 11: What is the horizontal asymptote of f(x)=2x2+3x2+5f(x) = \frac{2x^2 + 3}{x^2 + 5}f(x)=x2+52x2+3​?

Flashcard 12: What is the horizontal asymptote of f(x)=3x+22x2+5f(x) = \frac{3x + 2}{2x^2 + 5}f(x)=2x2+53x+2​?

Flashcard 13: What is the limit as xxx approaches infinity for f(x)=3x3+2x2+4f(x) = \frac{3x^3 + 2}{x^2 + 4}f(x)=x2+43x3+2​?

Flashcard 14: Determine limx→−∞−x3+43x3−x\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}limx→−∞​3x3−x−x3+4​.

Flashcard 15: Find the limit as xxx approaches infinity of f(x)=3x4x4+5f(x) = \frac{3x^4}{x^4 + 5}f(x)=x4+53x4​.

Flashcard 16: Determine limx→∞8x−32x+1\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}limx→∞​2x+18x−3​.

Flashcard 17: State the horizontal asymptote of f(x)=7x2−x3x2+2f(x) = \frac{7x^2 - x}{3x^2 + 2}f(x)=3x2+27x2−x​.

Flashcard 18: Find the horizontal asymptote of f(x)=5x3−2x4x3+xf(x) = \frac{5x^3 - 2x}{4x^3 + x}f(x)=4x3+x5x3−2x​.

Flashcard 19: Determine limx→−∞x2−2xx2+x\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}limx→−∞​x2+xx2−2x​.

Flashcard 20: What is the horizontal asymptote for f(x)=2x35x3−4f(x) = \frac{2x^3}{5x^3 - 4}f(x)=5x3−42x3​?

Flashcard 21: Determine limx→∞7x2−52x2+4\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}limx→∞​2x2+47x2−5​.

Flashcard 22: State the horizontal asymptote of f(x)=x2+xx3+1f(x) = \frac{x^2 + x}{x^3 + 1}f(x)=x3+1x2+x​.

Flashcard 23: What is the limit as xxx approaches infinity for f(x)=6x2−93x2+7f(x) = \frac{6x^2 - 9}{3x^2 + 7}f(x)=3x2+76x2−9​?

Flashcard 24: What is the horizontal asymptote of f(x)=x3−1x2+3xf(x) = \frac{x^3 - 1}{x^2 + 3x}f(x)=x2+3xx3−1​?

Flashcard 25: Find the limit as xxx approaches infinity of f(x)=4x22x2+3f(x) = \frac{4x^2}{2x^2 + 3}f(x)=2x2+34x2​.

Flashcard 26: State the horizontal asymptote of f(x)=5x23x2+2f(x) = \frac{5x^2}{3x^2 + 2}f(x)=3x2+25x2​.

Flashcard 27: What is the horizontal asymptote of f(x)=7x2x+3f(x) = \frac{7x}{2x + 3}f(x)=2x+37x​?

Flashcard 28: Determine limx→∞5x−12x+3\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}limx→∞​2x+35x−1​.

Flashcard 29: What is the horizontal asymptote of f(x)=4x3+5x3+6f(x) = \frac{4x^3 + 5}{x^3 + 6}f(x)=x3+64x3+5​?

Flashcard 30: What is the limit as xxx approaches infinity for f(x)=6x2−93x2+7f(x) = \frac{6x^2 - 9}{3x^2 + 7}f(x)=3x2+76x2−9​?

Flashcard 1: Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

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

Flashcard 3: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Flashcard 4: Determine $\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}$ .

Flashcard 5: Find the horizontal asymptote of $f(x) = \frac{x + 1}{x^2 + 1}$ .

Flashcard 6: State the horizontal asymptote of $f(x) = \frac{8x}{x^2 + 3}$ .

Flashcard 7: Find the limit as $x$ approaches infinity for $f(x) = \frac{7x^3}{2x^3 + 5}$ .

Flashcard 8: Find the horizontal asymptote of $f(x) = \frac{6x^3}{3x^3 + 1}$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 - 3}{2x^2 + x + 1}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{8x^3 + 1}{4x^3 + 2}$ ?

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 3}{x^2 + 5}$ ?

Flashcard 12: What is the horizontal asymptote of $f(x) = \frac{3x + 2}{2x^2 + 5}$ ?

Flashcard 13: What is the limit as $x$ approaches infinity for $f(x) = \frac{3x^3 + 2}{x^2 + 4}$ ?

Flashcard 14: Determine $\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}$ .

Flashcard 15: Find the limit as $x$ approaches infinity of $f(x) = \frac{3x^4}{x^4 + 5}$ .

Flashcard 16: Determine $\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}$ .

Flashcard 17: State the horizontal asymptote of $f(x) = \frac{7x^2 - x}{3x^2 + 2}$ .

Flashcard 18: Find the horizontal asymptote of $f(x) = \frac{5x^3 - 2x}{4x^3 + x}$ .

Flashcard 19: Determine $\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}$ .

Flashcard 20: What is the horizontal asymptote for $f(x) = \frac{2x^3}{5x^3 - 4}$ ?

Flashcard 21: Determine $\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}$ .

Flashcard 22: State the horizontal asymptote of $f(x) = \frac{x^2 + x}{x^3 + 1}$ .

Flashcard 23: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 - 1}{x^2 + 3x}$ ?

Flashcard 25: Find the limit as $x$ approaches infinity of $f(x) = \frac{4x^2}{2x^2 + 3}$ .

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

Flashcard 27: What is the horizontal asymptote of $f(x) = \frac{7x}{2x + 3}$ ?

Flashcard 28: Determine $\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Flashcard 30: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Flashcard 1: Determine $\lim_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

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

Flashcard 3: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Flashcard 4: Determine $\text{lim}_{x \to \infty} \frac{2x^3 - 5}{3x^3 + 1}$ .

Flashcard 5: Find the horizontal asymptote of $f(x) = \frac{x + 1}{x^2 + 1}$ .

Flashcard 6: State the horizontal asymptote of $f(x) = \frac{8x}{x^2 + 3}$ .

Flashcard 7: Find the limit as $x$ approaches infinity for $f(x) = \frac{7x^3}{2x^3 + 5}$ .

Flashcard 8: Find the horizontal asymptote of $f(x) = \frac{6x^3}{3x^3 + 1}$ .

Flashcard 9: State the horizontal asymptote of $f(x) = \frac{x^2 - 3}{2x^2 + x + 1}$ .

Flashcard 10: What is the horizontal asymptote of $f(x) = \frac{8x^3 + 1}{4x^3 + 2}$ ?

Flashcard 11: What is the horizontal asymptote of $f(x) = \frac{2x^2 + 3}{x^2 + 5}$ ?

Flashcard 12: What is the horizontal asymptote of $f(x) = \frac{3x + 2}{2x^2 + 5}$ ?

Flashcard 13: What is the limit as $x$ approaches infinity for $f(x) = \frac{3x^3 + 2}{x^2 + 4}$ ?

Flashcard 14: Determine $\text{lim}_{x \to -\infty} \frac{-x^3 + 4}{3x^3 - x}$ .

Flashcard 15: Find the limit as $x$ approaches infinity of $f(x) = \frac{3x^4}{x^4 + 5}$ .

Flashcard 16: Determine $\text{lim}_{x \to \infty} \frac{8x - 3}{2x + 1}$ .

Flashcard 17: State the horizontal asymptote of $f(x) = \frac{7x^2 - x}{3x^2 + 2}$ .

Flashcard 18: Find the horizontal asymptote of $f(x) = \frac{5x^3 - 2x}{4x^3 + x}$ .

Flashcard 19: Determine $\text{lim}_{x \to -\infty} \frac{x^2 - 2x}{x^2 + x}$ .

Flashcard 20: What is the horizontal asymptote for $f(x) = \frac{2x^3}{5x^3 - 4}$ ?

Flashcard 21: Determine $\text{lim}_{x \to \infty} \frac{7x^2 - 5}{2x^2 + 4}$ .

Flashcard 22: State the horizontal asymptote of $f(x) = \frac{x^2 + x}{x^3 + 1}$ .

Flashcard 23: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?

Flashcard 24: What is the horizontal asymptote of $f(x) = \frac{x^3 - 1}{x^2 + 3x}$ ?

Flashcard 25: Find the limit as $x$ approaches infinity of $f(x) = \frac{4x^2}{2x^2 + 3}$ .

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

Flashcard 27: What is the horizontal asymptote of $f(x) = \frac{7x}{2x + 3}$ ?

Flashcard 28: Determine $\text{lim}_{x \to \infty} \frac{5x - 1}{2x + 3}$ .

Flashcard 29: What is the horizontal asymptote of $f(x) = \frac{4x^3 + 5}{x^3 + 6}$ ?

Flashcard 30: What is the limit as $x$ approaches infinity for $f(x) = \frac{6x^2 - 9}{3x^2 + 7}$ ?