교과서 질문
Finding Limits
For the function f whose graph is given, determine the following limits. Write ∞ or −∞ where appropriate.
h. lim x → ∞ f(x)
313
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Ch. 2 - Limits and Continuity
Hass15th EditionThomas' CalculusISBN: 9780137616077
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TOC.tableOfContents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions490
- Ch. 8 - Techniques of Integration399
- Ch. 9 - First-Order Differential Equations66
- Ch. 10 - Infinite Sequences and Series132
- Ch. 11 - Parametric Equations and Polar Coordinates58
2장, 문제 2.4.2k
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
<IMAGE>
k. limx→3+ f(x) does not exist.
검증된 단계별 안내1
To determine if the limit \( \lim_{x \to 3^+} f(x) \) exists, we need to analyze the behavior of the function as \( x \) approaches 3 from the right side (i.e., values greater than 3).
Examine the graph of the function \( y = f(x) \) near \( x = 3 \). Look for the value that \( f(x) \) approaches as \( x \) gets closer to 3 from the right.
If the function approaches a specific finite value as \( x \to 3^+ \), then the limit exists and is equal to that value.
If the function does not approach a specific value (e.g., it oscillates or goes to infinity), then the limit does not exist.
Based on the graph, determine whether the function approaches a specific value or not as \( x \to 3^+ \), and conclude whether the statement is true or false.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Limits
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near points of interest, including points of discontinuity. Limits can be approached from the left (denoted as lim x→c-) or from the right (lim x→c+), which is crucial for analyzing one-sided limits.
추천 영상:
05:50
One-Sided Limits
Graphical Interpretation of Limits
Graphically, limits can be evaluated by observing the behavior of a function's graph as it approaches a specific x-value. If the function approaches a particular y-value from both sides, the limit exists. However, if the function approaches different values from the left and right, or if it does not approach any value at all, the limit may not exist.
추천 영상:
6:47Finding Limits Numerically and Graphically
Continuity and Discontinuity
A function is continuous at a point if the limit exists at that point and equals the function's value. Discontinuities can occur in various forms, such as removable, jump, or infinite discontinuities. Understanding the type of discontinuity present at a point is essential for determining the existence of limits and analyzing the function's behavior around that point.
추천 영상:
05:34Intro to Continuity
관련 실천
교과서 질문
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
<IMAGE>
g. limx→0+ f(x) = limx→0− f(x)
292
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교과서 질문
Which of the following statements about the function y=f(x) graphed here are true, and which are false?
h. f(0)=0
314
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교과서 질문
Limits and Continuity
Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
f. | ƒ(t) |
287
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교과서 질문
Limits and Continuity
Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
e. cos (g(t))
273
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교과서 질문
Which of the following statements about the function y=f(x) graphed here are true, and which are false?
g. limx→1 f(x) does not exist.
348
views