Mathematics Exam > Mathematics Questions > The set { 1/n Sin 1/ n: nEN } has a . only li...
Start Learning for Free
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.?
Most Upvoted Answer
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only l...
Answer:
To determine the limit points of the set {1/n sin(1/n): n ∈ N}, we need to find the values that the set approaches as n approaches infinity.
1. Evaluating the expression:
Let's evaluate the expression for a few values of n to understand the behavior of the set:
When n = 1: 1/1 sin(1/1) = 1 sin(1) ≈ 0.8415
When n = 2: 1/2 sin(1/2) = 1/2 sin(1/2) ≈ 0.4207
When n = 3: 1/3 sin(1/3) = 1/3 sin(1/3) ≈ 0.3473
...
2. Looking for patterns:
As n approaches infinity, we observe that the values of 1/n sin(1/n) are getting closer and closer to 0. However, there are also oscillations present in the values. To determine the limit points, we need to investigate the behavior of the set further.
3. Analyzing the oscillations:
Let's consider the function f(x) = sin(x)/x. As x approaches 0, f(x) approaches 1. This means that the values of sin(1/n)/(1/n) approach 1 as n approaches infinity. However, the additional factor of 1/n in the set {1/n sin(1/n): n ∈ N} causes the values to approach 0.
4. Identifying the limit points:
From the analysis above, we can conclude that the set {1/n sin(1/n): n ∈ N} has only one limit point, which is 0. The oscillations caused by the sin(1/n) term prevent the set from having any other limit points.
Therefore, the correct answer is (b) Only limit point its 0.
To determine the limit points of the set {1/n sin(1/n): n ∈ N}, we need to find the values that the set approaches as n approaches infinity.
1. Evaluating the expression:
Let's evaluate the expression for a few values of n to understand the behavior of the set:
When n = 1: 1/1 sin(1/1) = 1 sin(1) ≈ 0.8415
When n = 2: 1/2 sin(1/2) = 1/2 sin(1/2) ≈ 0.4207
When n = 3: 1/3 sin(1/3) = 1/3 sin(1/3) ≈ 0.3473
...
2. Looking for patterns:
As n approaches infinity, we observe that the values of 1/n sin(1/n) are getting closer and closer to 0. However, there are also oscillations present in the values. To determine the limit points, we need to investigate the behavior of the set further.
3. Analyzing the oscillations:
Let's consider the function f(x) = sin(x)/x. As x approaches 0, f(x) approaches 1. This means that the values of sin(1/n)/(1/n) approach 1 as n approaches infinity. However, the additional factor of 1/n in the set {1/n sin(1/n): n ∈ N} causes the values to approach 0.
4. Identifying the limit points:
From the analysis above, we can conclude that the set {1/n sin(1/n): n ∈ N} has only one limit point, which is 0. The oscillations caused by the sin(1/n) term prevent the set from having any other limit points.
Therefore, the correct answer is (b) Only limit point its 0.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.?
Question Description
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.?.
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.?.
Solutions for The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? defined & explained in the simplest way possible. Besides giving the explanation of
The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.?, a detailed solution for The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? has been provided alongside types of The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? theory, EduRev gives you an
ample number of questions to practice The set { 1/n Sin 1/ n: nEN } has a . only limit point its 1 b. only limit point its o C. only limit point its-1 d. there are three limit Point it 0,-1 , 1.? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup