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AP Calculus AB Flashcards: Algebraic Properties Of Limits

Study Algebraic Properties Of Limits 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 Algebraic Properties Of Limits, 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: Algebraic Properties Of Limits

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Tap or drag to reveal answer

ANSWER

The limit is $a$ . The identity function equals its input value.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Answer: The limit is $a$ . The identity function equals its input value.

Flashcard 2: Find $\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}$ . Use algebraic properties.

Answer: The limit is $6$ . Factor difference of squares: $\frac{(x+3)(x-3)}{x-3} = x+3$ .

Flashcard 3: Find $\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}$ . Use algebraic properties.

Answer: The limit is $\frac{1}{4}$ . Rationalize by multiplying by $\frac{\sqrt{x+2}+2}{\sqrt{x+2}+2}$ .

Flashcard 4: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Answer: The limit is $-4$ . Factor perfect square: $\frac{(x+2)^2}{x+2} = x+2$ , then substitute.

Flashcard 5: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Answer: The limit is $0$ . Factor both: $\frac{(x-1)(x+1)}{(x-1)(x+2)} = \frac{x+1}{x+2}$ , then substitute.

Flashcard 6: Find $\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)$ . Use algebraic properties.

Answer: The limit is $-3$ . Direct substitution: $3(1)^3 - 2(1)^2 + 1 - 5 = -3$ .

Flashcard 7: Find $\text{lim}_{x \to 0} x^2 \text{cos}(x)$ . Use algebraic properties.

Answer: The limit is $0$ . Product of limits: $\text{lim } x^2 \times \text{lim } \text{cos}(x) = 0 \times 1$ .

Flashcard 8: Find $\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)$ . Use algebraic properties.

Answer: The limit is $-2$ . Direct substitution: $(-1)^3 + 4(-1)^2 + (-1) - 6 = -2$ .

Flashcard 9: Find $\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}$ . Use known results.

Answer: The limit is $2$ . Use $\sin(2x) = 2\sin(x)\cos(x)$ and known limit $\sin(x)/x = 1$ .

Flashcard 10: Find $\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}$ . Use algebraic properties.

Answer: The limit is $-1$ . Factor: $\frac{(x-2)(x-3)}{x-2} = x-3$ , then substitute.

Flashcard 11: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Answer: The limit is $cL$ . Constant multiple property: factor out constants.

Flashcard 12: Find $\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}$ . Use algebraic properties.

Answer: The limit is $12$ . Factor difference of cubes: $\frac{(x-2)(x^2+2x+4)}{x-2} = x^2+2x+4$ .

Flashcard 13: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}$ . Use algebraic properties.

Answer: The limit is $2$ . Factor difference of squares: $\frac{(x+1)(x-1)}{x-1} = x+1$ .

Flashcard 14: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Answer: The limit is $c$ . Constants remain unchanged regardless of the input value.

Flashcard 15: What is the algebraic property of limits for the absolute value function?

Answer: $\lim_{x \to a} |f(x)| = |\lim_{x \to a} f(x)|$ . Absolute value of the limit equals limit of absolute value.

Flashcard 16: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Factor and cancel: $\frac{(x+2)(x-2)}{x-2} = x+2$ , then substitute.

Flashcard 17: Find $\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}$ . Use algebraic properties.

Answer: The limit is $8$ . Factor difference of squares: $\frac{(x+4)(x-4)}{x-4} = x+4$ .

Flashcard 18: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Rationalize by multiplying by $\frac{\sqrt{x}+2}{\sqrt{x}+2}$ .

Flashcard 19: If $\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} (f(x) + c)$ ?

Answer: The limit is $L + c$ . Sum property: limit of sum equals sum of limits.

Flashcard 20: Find $\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}$ . Use algebraic properties.

Answer: The limit is $3$ . Factor difference of cubes: $\frac{(x-1)(x^2+x+1)}{x-1} = x^2+x+1$ .

Flashcard 21: Find $\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}$ . Use known results.

Answer: The limit is $1$ . Reciprocal of the standard limit $\sin(x)/x = 1$ .

Flashcard 22: Find $\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}$ . Use algebraic properties.

Answer: The limit is $3$ . Rewrite as $\frac{\sin(3x)}{3x} \cdot \frac{3x}{x} \cdot \frac{x}{\sin(x)} = 1 \cdot 3 \cdot 1$ .

Flashcard 23: What is the limit of a power function: $\text{If }\lim_{x \to a} f(x) = L$ , what is $\lim_{x \to a} [f(x)]^n$ ?

Answer: The limit is $L^n$ . Power property: raise the limit to the same power.

Flashcard 24: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Answer: The limit is $-4$ . Factor perfect square: $\frac{(x+2)^2}{x+2} = x+2$ , then substitute.

Flashcard 25: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Answer: The limit is $cL$ . Constant multiple property: factor out constants.

Flashcard 26: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Factor and cancel: $\frac{(x+2)(x-2)}{x-2} = x+2$ , then substitute.

Flashcard 27: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Answer: The limit is $c$ . Constants remain unchanged regardless of the input value.

Flashcard 28: What is the algebraic property of limits for the absolute value function?

Answer: $\lim_{x \to a} |f(x)| = |\lim_{x \to a} f(x)|$ . Absolute value of the limit equals limit of absolute value.

Flashcard 29: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Rationalize by multiplying by $\frac{\sqrt{x}+2}{\sqrt{x}+2}$ .

Flashcard 30: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Answer: The limit is $0$ . Factor both: $\frac{(x-1)(x+1)}{(x-1)(x+2)} = \frac{x+1}{x+2}$ , then substitute.

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AP Calculus AB Flashcards: Algebraic Properties Of Limits

Study Algebraic Properties Of Limits 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 Algebraic Properties Of Limits, 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: Algebraic Properties Of Limits

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Tap or drag to reveal answer

ANSWER

The limit is $a$ . The identity function equals its input value.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Answer: The limit is $a$ . The identity function equals its input value.

Flashcard 2: Find $\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}$ . Use algebraic properties.

Answer: The limit is $6$ . Factor difference of squares: $\frac{(x+3)(x-3)}{x-3} = x+3$ .

Flashcard 3: Find $\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}$ . Use algebraic properties.

Answer: The limit is $\frac{1}{4}$ . Rationalize by multiplying by $\frac{\sqrt{x+2}+2}{\sqrt{x+2}+2}$ .

Flashcard 4: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Answer: The limit is $-4$ . Factor perfect square: $\frac{(x+2)^2}{x+2} = x+2$ , then substitute.

Flashcard 5: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Answer: The limit is $0$ . Factor both: $\frac{(x-1)(x+1)}{(x-1)(x+2)} = \frac{x+1}{x+2}$ , then substitute.

Flashcard 6: Find $\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)$ . Use algebraic properties.

Answer: The limit is $-3$ . Direct substitution: $3(1)^3 - 2(1)^2 + 1 - 5 = -3$ .

Flashcard 7: Find $\text{lim}_{x \to 0} x^2 \text{cos}(x)$ . Use algebraic properties.

Answer: The limit is $0$ . Product of limits: $\text{lim } x^2 \times \text{lim } \text{cos}(x) = 0 \times 1$ .

Flashcard 8: Find $\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)$ . Use algebraic properties.

Answer: The limit is $-2$ . Direct substitution: $(-1)^3 + 4(-1)^2 + (-1) - 6 = -2$ .

Flashcard 9: Find $\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}$ . Use known results.

Answer: The limit is $2$ . Use $\sin(2x) = 2\sin(x)\cos(x)$ and known limit $\sin(x)/x = 1$ .

Flashcard 10: Find $\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}$ . Use algebraic properties.

Answer: The limit is $-1$ . Factor: $\frac{(x-2)(x-3)}{x-2} = x-3$ , then substitute.

Flashcard 11: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Answer: The limit is $cL$ . Constant multiple property: factor out constants.

Flashcard 12: Find $\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}$ . Use algebraic properties.

Answer: The limit is $12$ . Factor difference of cubes: $\frac{(x-2)(x^2+2x+4)}{x-2} = x^2+2x+4$ .

Flashcard 13: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}$ . Use algebraic properties.

Answer: The limit is $2$ . Factor difference of squares: $\frac{(x+1)(x-1)}{x-1} = x+1$ .

Flashcard 14: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Answer: The limit is $c$ . Constants remain unchanged regardless of the input value.

Flashcard 15: What is the algebraic property of limits for the absolute value function?

Answer: $\lim_{x \to a} |f(x)| = |\lim_{x \to a} f(x)|$ . Absolute value of the limit equals limit of absolute value.

Flashcard 16: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Factor and cancel: $\frac{(x+2)(x-2)}{x-2} = x+2$ , then substitute.

Flashcard 17: Find $\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}$ . Use algebraic properties.

Answer: The limit is $8$ . Factor difference of squares: $\frac{(x+4)(x-4)}{x-4} = x+4$ .

Flashcard 18: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Rationalize by multiplying by $\frac{\sqrt{x}+2}{\sqrt{x}+2}$ .

Flashcard 19: If $\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} (f(x) + c)$ ?

Answer: The limit is $L + c$ . Sum property: limit of sum equals sum of limits.

Flashcard 20: Find $\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}$ . Use algebraic properties.

Answer: The limit is $3$ . Factor difference of cubes: $\frac{(x-1)(x^2+x+1)}{x-1} = x^2+x+1$ .

Flashcard 21: Find $\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}$ . Use known results.

Answer: The limit is $1$ . Reciprocal of the standard limit $\sin(x)/x = 1$ .

Flashcard 22: Find $\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}$ . Use algebraic properties.

Answer: The limit is $3$ . Rewrite as $\frac{\sin(3x)}{3x} \cdot \frac{3x}{x} \cdot \frac{x}{\sin(x)} = 1 \cdot 3 \cdot 1$ .

Flashcard 23: What is the limit of a power function: $\text{If }\lim_{x \to a} f(x) = L$ , what is $\lim_{x \to a} [f(x)]^n$ ?

Answer: The limit is $L^n$ . Power property: raise the limit to the same power.

Flashcard 24: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Answer: The limit is $-4$ . Factor perfect square: $\frac{(x+2)^2}{x+2} = x+2$ , then substitute.

Flashcard 25: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Answer: The limit is $cL$ . Constant multiple property: factor out constants.

Flashcard 26: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Factor and cancel: $\frac{(x+2)(x-2)}{x-2} = x+2$ , then substitute.

Flashcard 27: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Answer: The limit is $c$ . Constants remain unchanged regardless of the input value.

Flashcard 28: What is the algebraic property of limits for the absolute value function?

Answer: $\lim_{x \to a} |f(x)| = |\lim_{x \to a} f(x)|$ . Absolute value of the limit equals limit of absolute value.

Flashcard 29: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Answer: The limit is $4$ . Rationalize by multiplying by $\frac{\sqrt{x}+2}{\sqrt{x}+2}$ .

Flashcard 30: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Answer: The limit is $0$ . Factor both: $\frac{(x-1)(x+1)}{(x-1)(x+2)} = \frac{x+1}{x+2}$ , then substitute.

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AP Calculus AB Flashcards: Algebraic Properties Of Limits

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Algebraic Properties Of Limits

All flashcards

Flashcard 1: What is the limit of f(x)=xf(x) = xf(x)=x as xxx approaches aaa?

Flashcard 2: Find limx→3x2−9x−3\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}limx→3​x−3x2−9​. Use algebraic properties.

Flashcard 3: Find limx→2sqrt(x+2)−2x−2\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}limx→2​x−2sqrt(x+2)−2​. Use algebraic properties.

Flashcard 4: Find limx→−2x2+4x+4x+2\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}limx→−2​x+2x2+4x+4​. Use algebraic properties.

Flashcard 5: Find limx→1x2−1x2+x−2\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}limx→1​x2+x−2x2−1​. Use algebraic properties.

Flashcard 6: Find limx→1(3x3−2x2+x−5)\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)limx→1​(3x3−2x2+x−5). Use algebraic properties.

Flashcard 7: Find limx→0x2cos(x)\text{lim}_{x \to 0} x^2 \text{cos}(x)limx→0​x2cos(x). Use algebraic properties.

Flashcard 8: Find limx→−1(x3+4x2+x−6)\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)limx→−1​(x3+4x2+x−6). Use algebraic properties.

Flashcard 9: Find limx→0sin(2x)x\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}limx→0​xsin(2x)​. Use known results.

Flashcard 10: Find limx→2x2−5x+6x−2\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}limx→2​x−2x2−5x+6​. Use algebraic properties.

Flashcard 11: What is the limit property for a constant multiple: If limx→af(x)=L\text{If }\text{lim}_{x \to a} f(x) = LIf limx→a​f(x)=L, what is limx→a[cf(x)]\text{lim}_{x \to a} [cf(x)]limx→a​[cf(x)]?

Flashcard 12: Find limx→2x3−8x−2\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}limx→2​x−2x3−8​. Use algebraic properties.

Flashcard 13: Find limx→1x2−1x−1\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}limx→1​x−1x2−1​. Use algebraic properties.

Flashcard 14: What is the limit of a constant function f(x)=cf(x) = cf(x)=c as xxx approaches any value aaa?

Flashcard 15: What is the algebraic property of limits for the absolute value function?

Flashcard 16: Find limx→2x2−4x−2\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}limx→2​x−2x2−4​. Use algebraic properties.

Flashcard 17: Find limx→4x2−16x−4\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}limx→4​x−4x2−16​. Use algebraic properties.

Flashcard 18: Find limx→4x−4sqrt(x)−2\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}limx→4​sqrt(x)−2x−4​. Use algebraic properties.

Flashcard 19: If limx→af(x)=L\text{lim}_{x \to a} f(x) = Llimx→a​f(x)=L, what is limx→a(f(x)+c)\text{lim}_{x \to a} (f(x) + c)limx→a​(f(x)+c)?

Flashcard 20: Find limx→1x3−1x−1\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}limx→1​x−1x3−1​. Use algebraic properties.

Flashcard 21: Find limx→0xsin(x)\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}limx→0​sin(x)x​. Use known results.

Flashcard 22: Find limx→0sin(3x)sin(x)\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}limx→0​sin(x)sin(3x)​. Use algebraic properties.

Flashcard 23: What is the limit of a power function: If lim⁡x→af(x)=L\text{If }\lim_{x \to a} f(x) = LIf limx→a​f(x)=L, what is lim⁡x→a[f(x)]n\lim_{x \to a} [f(x)]^nlimx→a​[f(x)]n?

Flashcard 24: Find limx→−2x2+4x+4x+2\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}limx→−2​x+2x2+4x+4​. Use algebraic properties.

Flashcard 25: What is the limit property for a constant multiple: If limx→af(x)=L\text{If }\text{lim}_{x \to a} f(x) = LIf limx→a​f(x)=L, what is limx→a[cf(x)]\text{lim}_{x \to a} [cf(x)]limx→a​[cf(x)]?

Flashcard 26: Find limx→2x2−4x−2\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}limx→2​x−2x2−4​. Use algebraic properties.

Flashcard 27: What is the limit of a constant function f(x)=cf(x) = cf(x)=c as xxx approaches any value aaa?

Flashcard 28: What is the algebraic property of limits for the absolute value function?

Flashcard 29: Find limx→4x−4sqrt(x)−2\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}limx→4​sqrt(x)−2x−4​. Use algebraic properties.

Flashcard 30: Find limx→1x2−1x2+x−2\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}limx→1​x2+x−2x2−1​. Use algebraic properties.

Opening subject page...

AP Calculus AB Flashcards: Algebraic Properties Of Limits

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Algebraic Properties Of Limits

All flashcards

Flashcard 1: What is the limit of f(x)=xf(x) = xf(x)=x as xxx approaches aaa?

Flashcard 2: Find limx→3x2−9x−3\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}limx→3​x−3x2−9​. Use algebraic properties.

Flashcard 3: Find limx→2sqrt(x+2)−2x−2\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}limx→2​x−2sqrt(x+2)−2​. Use algebraic properties.

Flashcard 4: Find limx→−2x2+4x+4x+2\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}limx→−2​x+2x2+4x+4​. Use algebraic properties.

Flashcard 5: Find limx→1x2−1x2+x−2\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}limx→1​x2+x−2x2−1​. Use algebraic properties.

Flashcard 6: Find limx→1(3x3−2x2+x−5)\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)limx→1​(3x3−2x2+x−5). Use algebraic properties.

Flashcard 7: Find limx→0x2cos(x)\text{lim}_{x \to 0} x^2 \text{cos}(x)limx→0​x2cos(x). Use algebraic properties.

Flashcard 8: Find limx→−1(x3+4x2+x−6)\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)limx→−1​(x3+4x2+x−6). Use algebraic properties.

Flashcard 9: Find limx→0sin(2x)x\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}limx→0​xsin(2x)​. Use known results.

Flashcard 10: Find limx→2x2−5x+6x−2\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}limx→2​x−2x2−5x+6​. Use algebraic properties.

Flashcard 11: What is the limit property for a constant multiple: If limx→af(x)=L\text{If }\text{lim}_{x \to a} f(x) = LIf limx→a​f(x)=L, what is limx→a[cf(x)]\text{lim}_{x \to a} [cf(x)]limx→a​[cf(x)]?

Flashcard 12: Find limx→2x3−8x−2\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}limx→2​x−2x3−8​. Use algebraic properties.

Flashcard 13: Find limx→1x2−1x−1\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}limx→1​x−1x2−1​. Use algebraic properties.

Flashcard 14: What is the limit of a constant function f(x)=cf(x) = cf(x)=c as xxx approaches any value aaa?

Flashcard 15: What is the algebraic property of limits for the absolute value function?

Flashcard 16: Find limx→2x2−4x−2\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}limx→2​x−2x2−4​. Use algebraic properties.

Flashcard 17: Find limx→4x2−16x−4\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}limx→4​x−4x2−16​. Use algebraic properties.

Flashcard 18: Find limx→4x−4sqrt(x)−2\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}limx→4​sqrt(x)−2x−4​. Use algebraic properties.

Flashcard 19: If limx→af(x)=L\text{lim}_{x \to a} f(x) = Llimx→a​f(x)=L, what is limx→a(f(x)+c)\text{lim}_{x \to a} (f(x) + c)limx→a​(f(x)+c)?

Flashcard 20: Find limx→1x3−1x−1\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}limx→1​x−1x3−1​. Use algebraic properties.

Flashcard 21: Find limx→0xsin(x)\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}limx→0​sin(x)x​. Use known results.

Flashcard 22: Find limx→0sin(3x)sin(x)\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}limx→0​sin(x)sin(3x)​. Use algebraic properties.

Flashcard 23: What is the limit of a power function: If lim⁡x→af(x)=L\text{If }\lim_{x \to a} f(x) = LIf limx→a​f(x)=L, what is lim⁡x→a[f(x)]n\lim_{x \to a} [f(x)]^nlimx→a​[f(x)]n?

Flashcard 24: Find limx→−2x2+4x+4x+2\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}limx→−2​x+2x2+4x+4​. Use algebraic properties.

Flashcard 25: What is the limit property for a constant multiple: If limx→af(x)=L\text{If }\text{lim}_{x \to a} f(x) = LIf limx→a​f(x)=L, what is limx→a[cf(x)]\text{lim}_{x \to a} [cf(x)]limx→a​[cf(x)]?

Flashcard 26: Find limx→2x2−4x−2\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}limx→2​x−2x2−4​. Use algebraic properties.

Flashcard 27: What is the limit of a constant function f(x)=cf(x) = cf(x)=c as xxx approaches any value aaa?

Flashcard 28: What is the algebraic property of limits for the absolute value function?

Flashcard 29: Find limx→4x−4sqrt(x)−2\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}limx→4​sqrt(x)−2x−4​. Use algebraic properties.

Flashcard 30: Find limx→1x2−1x2+x−2\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}limx→1​x2+x−2x2−1​. Use algebraic properties.

Flashcard 1: What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Flashcard 2: Find $\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}$ . Use algebraic properties.

Flashcard 3: Find $\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}$ . Use algebraic properties.

Flashcard 4: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Flashcard 5: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Flashcard 6: Find $\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)$ . Use algebraic properties.

Flashcard 7: Find $\text{lim}_{x \to 0} x^2 \text{cos}(x)$ . Use algebraic properties.

Flashcard 8: Find $\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)$ . Use algebraic properties.

Flashcard 9: Find $\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}$ . Use known results.

Flashcard 10: Find $\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}$ . Use algebraic properties.

Flashcard 11: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Flashcard 12: Find $\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}$ . Use algebraic properties.

Flashcard 13: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}$ . Use algebraic properties.

Flashcard 14: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Flashcard 16: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Flashcard 17: Find $\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}$ . Use algebraic properties.

Flashcard 18: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Flashcard 19: If $\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} (f(x) + c)$ ?

Flashcard 20: Find $\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}$ . Use algebraic properties.

Flashcard 21: Find $\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}$ . Use known results.

Flashcard 22: Find $\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}$ . Use algebraic properties.

Flashcard 23: What is the limit of a power function: $\text{If }\lim_{x \to a} f(x) = L$ , what is $\lim_{x \to a} [f(x)]^n$ ?

Flashcard 24: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Flashcard 25: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Flashcard 26: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Flashcard 27: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Flashcard 29: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Flashcard 30: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Flashcard 1: What is the limit of $f(x) = x$ as $x$ approaches $a$ ?

Flashcard 2: Find $\text{lim}_{x \to 3} \frac{x^2 - 9}{x - 3}$ . Use algebraic properties.

Flashcard 3: Find $\text{lim}_{x \to 2} \frac{\text{sqrt}(x+2) - 2}{x - 2}$ . Use algebraic properties.

Flashcard 4: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Flashcard 5: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.

Flashcard 6: Find $\text{lim}_{x \to 1} (3x^3 - 2x^2 + x - 5)$ . Use algebraic properties.

Flashcard 7: Find $\text{lim}_{x \to 0} x^2 \text{cos}(x)$ . Use algebraic properties.

Flashcard 8: Find $\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)$ . Use algebraic properties.

Flashcard 9: Find $\text{lim}_{x \to 0} \frac{\text{sin}(2x)}{x}$ . Use known results.

Flashcard 10: Find $\text{lim}_{x \to 2} \frac{x^2 - 5x + 6}{x - 2}$ . Use algebraic properties.

Flashcard 11: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Flashcard 12: Find $\text{lim}_{x \to 2} \frac{x^3 - 8}{x - 2}$ . Use algebraic properties.

Flashcard 13: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x - 1}$ . Use algebraic properties.

Flashcard 14: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Flashcard 16: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Flashcard 17: Find $\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}$ . Use algebraic properties.

Flashcard 18: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Flashcard 19: If $\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} (f(x) + c)$ ?

Flashcard 20: Find $\text{lim}_{x \to 1} \frac{x^3 - 1}{x - 1}$ . Use algebraic properties.

Flashcard 21: Find $\text{lim}_{x \to 0} \frac{x}{\text{sin}(x)}$ . Use known results.

Flashcard 22: Find $\text{lim}_{x \to 0} \frac{\text{sin}(3x)}{\text{sin}(x)}$ . Use algebraic properties.

Flashcard 23: What is the limit of a power function: $\text{If }\lim_{x \to a} f(x) = L$ , what is $\lim_{x \to a} [f(x)]^n$ ?

Flashcard 24: Find $\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}$ . Use algebraic properties.

Flashcard 25: What is the limit property for a constant multiple: $\text{If }\text{lim}_{x \to a} f(x) = L$ , what is $\text{lim}_{x \to a} [cf(x)]$ ?

Flashcard 26: Find $\text{lim}_{x \to 2} \frac{x^2 - 4}{x - 2}$ . Use algebraic properties.

Flashcard 27: What is the limit of a constant function $f(x) = c$ as $x$ approaches any value $a$ ?

Flashcard 29: Find $\text{lim}_{x \to 4} \frac{x - 4}{\text{sqrt}(x) - 2}$ . Use algebraic properties.

Flashcard 30: Find $\text{lim}_{x \to 1} \frac{x^2 - 1}{x^2 + x - 2}$ . Use algebraic properties.