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Questions and Answers
Find the exact limit of $\lim_{x \to 4} (x + x^2 + 1)$
Find the exact limit of $\lim_{x \to 4} (x + x^2 + 1)$
21
Find the exact limit of $\lim_{x \to 3} \frac{x}{x-3}$
Find the exact limit of $\lim_{x \to 3} \frac{x}{x-3}$
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Find the exact limit of $\lim_{x \to -\infty} \frac{x^2 + 4 + x}{x^2 - 4x + 3}$
Find the exact limit of $\lim_{x \to -\infty} \frac{x^2 + 4 + x}{x^2 - 4x + 3}$
1
Find the exact limit of $\lim_{x \to \infty} \frac{x^2 + 4 - x}{x^2 - 4x + 3}$
Find the exact limit of $\lim_{x \to \infty} \frac{x^2 + 4 - x}{x^2 - 4x + 3}$
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Find the exact limit of $\lim_{x \to 5} \frac{x^{10} - x^5 + 1}{2x^{10} - 7}$
Find the exact limit of $\lim_{x \to 5} \frac{x^{10} - x^5 + 1}{2x^{10} - 7}$
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Find the exact limit of $\lim_{x \to -\infty} \frac{(x-2)(x-3)(2x+5)(x-10)}{(x-3)(3x+7)(x^2-4)}$
Find the exact limit of $\lim_{x \to -\infty} \frac{(x-2)(x-3)(2x+5)(x-10)}{(x-3)(3x+7)(x^2-4)}$
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Find the exact limit of $\lim_{x \to 0} \frac{x^2 - 4}{x^2 + 2x - 8}$
Find the exact limit of $\lim_{x \to 0} \frac{x^2 - 4}{x^2 + 2x - 8}$
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Which of the following statements are true about the limit of the function f(x) shown in the graph?
Which of the following statements are true about the limit of the function f(x) shown in the graph?
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Find the limit of $\lim_{x \to 4} f(x)$ for the piecewise function $f(x) = \begin{cases} \ln(3x), & 0 < x \leq 3 \ \frac{x}{\ln(3)}, & 3 < x \leq 4 \end{cases}$
Find the limit of $\lim_{x \to 4} f(x)$ for the piecewise function $f(x) = \begin{cases} \ln(3x), & 0 < x \leq 3 \ \frac{x}{\ln(3)}, & 3 < x \leq 4 \end{cases}$
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Find the limit of $\lim_{x \to -1^-} f(x)$ for the function f(x) shown in the graph.
Find the limit of $\lim_{x \to -1^-} f(x)$ for the function f(x) shown in the graph.
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Find the limit of $\lim_{x \to -1^+} f(x)$ for the function f(x) shown in the graph.
Find the limit of $\lim_{x \to -1^+} f(x)$ for the function f(x) shown in the graph.
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Find the limit of $\lim_{x \to 2} f(x)$ for the function f(x) shown in the graph.
Find the limit of $\lim_{x \to 2} f(x)$ for the function f(x) shown in the graph.
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Find the limit of $\lim_{x \to -\infty} \frac{ax^2 - 1}{x^2 - 9}$ where $x < 3$
Find the limit of $\lim_{x \to -\infty} \frac{ax^2 - 1}{x^2 - 9}$ where $x < 3$
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Find the values of a and b that make the function f(x) continuous at x = 3, where $f(x) = 2a - 3b$ for x = 3
Find the values of a and b that make the function f(x) continuous at x = 3, where $f(x) = 2a - 3b$ for x = 3
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To make the function f(x) = $\frac{x^2 - 1}{x - 1}$ continuous at x = 1, what must be the value of f(1)?
To make the function f(x) = $\frac{x^2 - 1}{x - 1}$ continuous at x = 1, what must be the value of f(1)?
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If $f(x) = \frac{(x+2)(x+3)(x-7)}{x^2 - 9}$, then f(x) has a removable discontinuity at x = -3.
If $f(x) = \frac{(x+2)(x+3)(x-7)}{x^2 - 9}$, then f(x) has a removable discontinuity at x = -3.
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Study Notes
Limits
- There are 20 limit questions, each with a unique function and limit operation (e.g., x approaches positive infinity, negative infinity, or a specific value)
- Examples of functions include rational functions, polynomial functions, and trigonometric functions
Graph Analysis
- Question 2 involves analyzing the graph of f(x) to determine which statements are true about the limits of the function at x = 1
- The graph is not provided, but the student is expected to understand the properties of the function based on the given statements
Piecewise Functions
- Question 3 involves a piecewise function with two parts, each defined for a specific domain
- The student is asked to find the limit of the function as x approaches 3
Graph of Function
- Question 4 involves finding the limits of a function based on its graph
- The graph is not provided, but the student is expected to understand the properties of the function based on the given limits
Continuity
- Question 5 involves finding the values of a and b that make the function f(x) continuous at x = 3
- The function is defined piecewise, with two parts, each defined for a specific domain
Function Analysis
- Question 6 involves analyzing the function f(x) to determine the value of f(1) for the function to be continuous at x = 1
- The function is defined as x^2 - 1 / x - 1, except at x = 1
Discontinuity
- Question 7 involves analyzing the function f(x) to determine the type of discontinuity at x = -3 and x = 3
- The function is defined as (x + 2)(x + 3)(x - 7) / x^2 - 9
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Description
Practice quiz reviewing limits in pre-calculus, covering algebraic limits and infinite limits in chapter 13.
