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Ch. 2 - Limits
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 2 - Limits문제 2.4.7c
2장, 문제 2.4.7c

The graph of f in the figure has vertical asymptotes at x=1 and x=2. Analyze the following limits. <IMAGE>
lim x→1 f(x)

검증된 단계별 안내
1
Identify the behavior of the function \( f(x) \) as \( x \) approaches 1 from the left (\( x \to 1^- \)).
Identify the behavior of the function \( f(x) \) as \( x \) approaches 1 from the right (\( x \to 1^+ \)).
Determine if the left-hand limit and the right-hand limit as \( x \to 1 \) are equal or not.
If the left-hand limit and right-hand limit are not equal, conclude that the limit \( \lim_{x \to 1} f(x) \) does not exist.
If the left-hand limit and right-hand limit are equal, state that the limit \( \lim_{x \to 1} f(x) \) is equal to that common value.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m
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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 f has vertical asymptotes at x=1 and x=2, indicating that as x approaches these values, f(x) does not settle at a finite limit but instead diverges.
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 vertical asymptotes, the limit of f(x) as x approaches 1 or 2 will help determine whether f(x) approaches positive or negative infinity, which is crucial for understanding the function's behavior near these points.
추천 영상:
05:50
One-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 the left or the right. For the limits as x approaches 1, it is important to evaluate both the left-hand limit (as x approaches 1 from values less than 1) and the right-hand limit (as x approaches 1 from values greater than 1) to fully understand the function's behavior at the asymptote.
추천 영상:
05:50
One-Sided Limits
관련 실천
교과서 질문

For the following position functions, make a table of average velocities similar to those in Exercises 19–20 and make a conjecture about the instantaneous velocity at the indicated time. 


c. s(t)=40 sin 2t at t=0

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교과서 질문

Determine the following limits.


b. limx→2−1x(x−2){\(\displaystyle\]\lim\)_{x\(\to\)2^{-}}}\(\frac{1}{\sqrt{x\left(x-2\right)}\)}

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교과서 질문

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a- f(x) and lim x→a+ f(x).

f(x) = (x^4−1)/(x^2−1)

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교과서 질문

Complete the following steps for the given functions. 


c. Graph ff and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.


f(x)=x2−3x+6f\(\left\)(x\(\right\))=\(\frac{x^2-3}{x+6}\)

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교과서 질문

Complete the following steps for the given functions. 


c. Graph f and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.


f(x)=x2−2x+53x−2f\(\left\)(x\(\right\))=\(\frac{x^2-2x+5}{3x-2}\)

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교과서 질문

A projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.


b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t=a.

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