교과서 질문
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
294
views
Ch. 2 - Limits and Continuity
Hass15th EditionThomas' CalculusISBN: 9780137616077
Not the one you use?Change textbookSelect a different textbook
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 1c
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
검증된 단계별 안내1
To determine the limit \( \lim_{x \to 0^-} f(x) \), we need to analyze the behavior of the function \( f(x) \) as \( x \) approaches 0 from the left side (negative side).
Examine the graph of the function \( y = f(x) \) and observe the values of \( f(x) \) as \( x \) gets closer to 0 from the left.
Identify the y-value that \( f(x) \) approaches as \( x \) approaches 0 from the left. This is the value of the left-hand limit.
If the y-value that \( f(x) \) approaches is 0, then the statement \( \lim_{x \to 0^-} f(x) = 0 \) is true. Otherwise, it is false.
Conclude whether the statement is true or false based on the observed behavior of the function on the graph.
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 specific points, even if they are not defined at those points. For example, the limit of f(x) as x approaches 0 from the left (denoted as lim x→0− f(x)) examines the values f(x) takes as x gets closer to 0 from negative values.
추천 영상:
05:50
One-Sided Limits
One-Sided Limits
One-sided limits refer to the limits of a function as the input approaches a specific value from one side only, either the left or the right. The notation lim x→a− f(x) indicates the limit as x approaches 'a' from the left, while lim x→a+ f(x) indicates the limit from the right. Understanding one-sided limits is crucial for analyzing functions that may have different behaviors on either side of 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 specific point. By observing the behavior of the graph near that point, one can infer the limit. This visual approach is particularly useful for identifying discontinuities or jumps in the function, which can affect the existence of 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?
j. limx→2− f(x) = 2
268
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?
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