16 Questions
Find the exact limit of $\lim_{x \to 4} (x + x^2 + 1)$
21
Find the exact limit of $\lim_{x \to 3} \frac{x}{x-3}$
undefined
Find the exact limit of $\lim_{x \to -\infty} \frac{x^2 + 4 + x}{x^2 - 4x + 3}$
1
Find the exact limit of $\lim_{x \to \infty} \frac{x^2 + 4 - x}{x^2 - 4x + 3}$
1
Find the exact limit of $\lim_{x \to 5} \frac{x^{10} - x^5 + 1}{2x^{10} - 7}$
undefined
Find the exact limit of $\lim_{x \to -\infty} \frac{(x-2)(x-3)(2x+5)(x-10)}{(x-3)(3x+7)(x^2-4)}$
undefined
Find the exact limit of $\lim_{x \to 0} \frac{x^2 - 4}{x^2 + 2x - 8}$
2
Which of the following statements are true about the limit of the function f(x) shown in the graph?
I and II only
Find the limit of $\lim_{x \to 4} f(x)$ for the piecewise function $f(x) = \begin{cases} \ln(3x), & 0 < x \leq 3 \ \frac{x}{\ln(3)}, & 3 < x \leq 4 \end{cases}$
ln 27
Find the limit of $\lim_{x \to -1^-} f(x)$ for the function f(x) shown in the graph.
2
Find the limit of $\lim_{x \to -1^+} f(x)$ for the function f(x) shown in the graph.
3
Find the limit of $\lim_{x \to 2} f(x)$ for the function f(x) shown in the graph.
4
Find the limit of $\lim_{x \to -\infty} \frac{ax^2 - 1}{x^2 - 9}$ where $x < 3$
a
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
a = 2, b = 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)?
2
If $f(x) = \frac{(x+2)(x+3)(x-7)}{x^2 - 9}$, then f(x) has a removable discontinuity at x = -3.
True
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
Practice quiz reviewing limits in pre-calculus, covering algebraic limits and infinite limits in chapter 13.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
