Textbook Question
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→3 f(x)
2
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Ch. 2 - Limits
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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Table of contents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
Chapter 2, Problem 4i
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→3^+ f(x)
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Identify the behavior of the function \( f(x) \) as \( x \) approaches 3 from the right (denoted as \( x \to 3^+ \)).
Examine the graph of \( f(x) \) to observe the values of \( f(x) \) as \( x \) gets closer to 3 from values greater than 3.
Look for any discontinuities, jumps, or asymptotic behavior near \( x = 3 \) to understand how \( f(x) \) behaves.
Determine the value that \( f(x) \) approaches as \( x \to 3^+ \) by observing the trend on the graph.
Conclude the limit \( \lim_{x \to 3^+} f(x) \) based on the observed behavior of the function on the graph.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Limits
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. In this case, we are interested in the limit of f(x) as x approaches 3 from the right (denoted as x→3^+). Understanding limits helps in analyzing the continuity and behavior of functions at specific points.
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One-Sided Limits
One-Sided Limits
One-sided limits refer to the value that a function approaches as the input approaches a specific point from one side only. The notation x→3^+ indicates that we are looking at values of x that are greater than 3. This is crucial for determining the behavior of f(x) near x = 3, especially if the function has different behaviors from the left and right.
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Graphical Analysis
Graphical analysis involves interpreting the visual representation of a function to understand its properties, such as limits, continuity, and discontinuities. By examining the graph of f near x = 3, one can determine the value of the limit as x approaches 3 from the right, which is essential for solving the given problem.
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Related Practice
Textbook Question
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
f(1)
Textbook Question
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→3^− f(x)
1
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Textbook Question
Determine the following limits at infinity.
lim x→ ∞ x^−6
1
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Textbook Question
Use the graph of in the figure to find the following values or state that they do not exist. <IMAGE>
Textbook Question
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→1 f(x)