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Ch. 2 - Limits
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
All textbooksBriggs 3rd EditionCh. 2 - LimitsProblem 4b
Chapter 2, Problem 4b

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→−1^− f(x)

Verified step by step guidance
1
Identify the type of limit: The problem asks for the left-hand limit of the function \( f(x) \) as \( x \) approaches \(-1\). This is denoted as \( \lim_{{x \to -1^-}} f(x) \).
Understand the notation: The notation \( x \to -1^- \) means that \( x \) is approaching \(-1\) from the left side, or from values less than \(-1\).
Examine the graph: Look at the behavior of the function \( f(x) \) as \( x \) gets closer to \(-1\) from the left. Observe the y-values that \( f(x) \) approaches.
Determine the limit: Based on the graph, identify the value that \( f(x) \) approaches as \( x \) approaches \(-1\) from the left.
Conclude the analysis: State the left-hand limit of \( f(x) \) as \( x \) approaches \(-1\) based on your observations from 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 left-hand limit as x approaches -1, denoted as lim x→−1^− f(x). This means we examine the values of f(x) as x gets closer to -1 from the left side, which helps us understand the function's behavior at that point.
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Left-Hand Limit

The left-hand limit refers specifically to the value that a function approaches as the input approaches a certain point from the left. It is denoted as lim x→c^− f(x) for a function f(x) as x approaches c. This concept is crucial for evaluating limits at points where the function may not be defined or may behave differently from the right-hand side.
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Graphical Analysis

Graphical analysis involves using the visual representation of a function to understand its behavior, including limits, continuity, and discontinuities. By examining the graph of f, one can identify the value that f(x) approaches as x approaches -1 from the left, which is essential for accurately evaluating the limit in the given question.
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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 hh in the figure to find the following values or state that they do not exist. <IMAGE>

h(4)h\(\left\)(4\(\right\))

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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)

2
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Textbook Question

Use the graph of hh in the figure to find the following values or state that they do not exist. <IMAGE>

limx→4h(x){\(\displaystyle\]\lim\)_{x\(\to\)4}h\(\left\)(x\(\right\))}

1
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Textbook Question

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

f(−1)

5
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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)