JEE Exam > JEE Questions > Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0,...
Start Learning for Free
Consider f (x) = x2 /| x | , x ≠ 0, f(x) = 0, x = 0
- a)f(x) is discontinuous everywhere
- b)f(x) is continuous everywhere
- c)f ′ (x) exists in − 1,1
- d)f ′ (x) exists in − 2,2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontin...
Explanation:
Continuity of f(x):
- The function f(x) is defined as f(x) = x^2 / |x| for x ≠ 0 and f(x) = 0 for x = 0.
- For x ≠ 0, f(x) = x^2 / |x| = x. As x approaches 0 from the left, f(x) approaches 0. Similarly, as x approaches 0 from the right, f(x) approaches 0.
- Therefore, the limit of f(x) as x approaches 0 exists and is equal to 0, which is also the value of f(x) at x = 0.
- Hence, f(x) is continuous at x = 0.
Continuity Everywhere:
- For x ≠ 0, f(x) = x^2 / |x| = x, which is a continuous function everywhere except at x = 0.
- At x = 0, f(x) is defined separately as 0, which is also a continuous function at x = 0.
- Therefore, f(x) is continuous everywhere.
Conclusion:
- The correct answer is option 'B' which states that f(x) is continuous everywhere.
Continuity of f(x):
- The function f(x) is defined as f(x) = x^2 / |x| for x ≠ 0 and f(x) = 0 for x = 0.
- For x ≠ 0, f(x) = x^2 / |x| = x. As x approaches 0 from the left, f(x) approaches 0. Similarly, as x approaches 0 from the right, f(x) approaches 0.
- Therefore, the limit of f(x) as x approaches 0 exists and is equal to 0, which is also the value of f(x) at x = 0.
- Hence, f(x) is continuous at x = 0.
Continuity Everywhere:
- For x ≠ 0, f(x) = x^2 / |x| = x, which is a continuous function everywhere except at x = 0.
- At x = 0, f(x) is defined separately as 0, which is also a continuous function at x = 0.
- Therefore, f(x) is continuous everywhere.
Conclusion:
- The correct answer is option 'B' which states that f(x) is continuous everywhere.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer?
Question Description
Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer?.
Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer?.
Solutions for Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider f (x)= x2/| x | , x ≠ 0, f(x)= 0, x = 0a)f(x) is discontinuous everywhereb)f(x) is continuous everywherec)f ′ (x)exists in − 1,1d)f ′ (x)exists in − 2,2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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