Textbook Question
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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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 4h
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→3^− f(x)
Verified step by step guidance1
Identify the point of interest, which is x = 3, and note that the limit is from the left (x → 3^−).
Examine the graph of the function f(x) as x approaches 3 from values less than 3.
Observe the behavior of f(x) as x gets closer to 3 from the left side. Look for the y-value that f(x) approaches.
Determine if the function approaches a specific value, or if it diverges or has a discontinuity at x = 3.
Conclude the limit by stating the y-value that f(x) approaches as x approaches 3 from the left.
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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. Specifically, the notation lim x→a f(x) indicates the value that f(x) approaches as x gets arbitrarily close to a from either the left (denoted as 3^−) or the right. Understanding limits is crucial for analyzing continuity, derivatives, and integrals.
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One-Sided Limits
One-Sided Limits
One-sided limits refer to the evaluation of a limit from one direction only. The notation lim x→a^− f(x) signifies the limit of f(x) as x approaches a from the left side. This concept is particularly important when dealing with functions that may have different behaviors or discontinuities at a specific point.
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Graphical Analysis
Graphical analysis involves interpreting the visual representation of a function to understand its behavior, including limits, continuity, and asymptotic behavior. By examining the graph of f near the point of interest (x=3), one can determine the value that f(x) approaches as x approaches 3 from the left, which is essential for evaluating the limit.
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Related Practice
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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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Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
f(1)
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Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→−1 f(x)
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Textbook Question
Determine the following limits at infinity.
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1
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Textbook Question
Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→1 f(x)