교과서 질문
The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>
lim x→3^+ h(x)
237
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Ch. 2 - Limits
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- 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
2장, 문제 2.4.9f
The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>
lim x→3 h(x)
검증된 단계별 안내1
Step 1: Identify the type of limit problem. Since the limit is approaching a point where there is a vertical asymptote (x = 3), this is a limit involving a vertical asymptote.
Step 2: Understand the behavior of the function near the asymptote. As x approaches 3, the function h(x) will tend to either positive infinity or negative infinity, depending on the direction from which x approaches 3.
Step 3: Consider the one-sided limits. Evaluate the limit from the left (x → 3⁻) and from the right (x → 3⁺) separately to determine the behavior of h(x) as it approaches the asymptote.
Step 4: Analyze the graph. Look at the graph of h(x) near x = 3 to see if the function approaches positive or negative infinity from either side.
Step 5: Conclude the limit. Based on the behavior observed in the graph, determine if the two one-sided limits are equal or if they differ, which will indicate whether the overall limit exists or not.
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.
Vertical Asymptotes
Vertical asymptotes occur in the graph of a function where the function approaches infinity or negative infinity as the input approaches a certain value. In this case, the function h has vertical asymptotes at x = -2 and x = 3, indicating that as x approaches these values, h(x) will not approach a finite limit.
추천 영상:
가이드 코스
3:40
Introduction to Cotangent Graph Example 1
Limits
A limit describes the behavior of a function as the input approaches a particular value. In the context of the question, evaluating the limit as x approaches 3 for h(x) involves determining how h(x) behaves near the vertical asymptote at x = 3, which typically results in the limit being either positive or negative infinity.
추천 영상:
05:50One-Sided Limits
One-Sided Limits
One-sided limits are used to analyze the behavior of a function as it approaches a specific point from one side only, either from the left (denoted as lim x→c-) or from the right (denoted as lim x→c+). For the limit as x approaches 3, it is essential to consider both one-sided limits to fully understand the behavior of h(x) near the vertical asymptote.
추천 영상:
05:50One-Sided Limits
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