교과서 질문
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
c. limx→0− f(x) = 0
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Ch. 2 - Limits and Continuity
Hass15th EditionThomas' CalculusISBN: 9780137616077
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Table of contents
- 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 Functions489
- Ch. 8 - Techniques of Integration398
- Ch. 9 - First-Order Differential Equations60
- Ch. 10 - Infinite Sequences and Series119
- Ch. 11 - Parametric Equations and Polar Coordinates58
2장, 문제 1a
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
a. limx→−1+ f(x) = 1
검증된 단계별 안내1
Examine the graph of the function y = f(x) as x approaches -1 from the right (x → -1+). This means you should look at the values of f(x) as x gets closer to -1 from values greater than -1.
Identify the y-value that the function approaches as x approaches -1 from the right. This is the value of the right-hand limit, limx→−1+ f(x).
Check if the y-value that the function approaches as x approaches -1 from the right is equal to 1.
If the y-value is equal to 1, then the statement limx→−1+ f(x) = 1 is true. Otherwise, it is false.
Conclude whether the statement is true or false based on the y-value identified in the previous steps.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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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. For example, limx→−1+ f(x) refers to the limit of f(x) as x approaches -1 from the right side.
추천 영상:
05:50
One-Sided Limits
One-Sided Limits
One-sided limits are limits that consider the behavior of a function as the input approaches a specific value from one direction only. The notation limx→−1+ f(x) indicates the limit as x approaches -1 from the right (values greater than -1). This is crucial for analyzing functions that may behave differently from the left and right at a point.
추천 영상:
05:50One-Sided Limits
Graphical Interpretation of Limits
Graphical interpretation of limits involves analyzing the graph of a function to determine the value that the function approaches as the input approaches a certain point. By observing the graph near x = -1, one can visually assess whether the function approaches a specific value, which aids in confirming or refuting statements about limits.
추천 영상:
6:47Finding Limits Numerically and Graphically
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?
f. limx→0 f(x) = 0
343
views
교과서 질문
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
e. limx→0 f(x) exists
324
views