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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : f(x) = [x] is not differentiable at x = 2.
Reason : f(x) = [x] is not continuous at x = 2.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
F(x) = [x] is not continuous when x is an integer.
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So f(x) is not continuous at x = 2. Hence R is true.
A differentiable function is always continuous.
Since f(x) = [x] is not continuous at x = 2, it is also not differentiable at x = 2.
Hence A is true.
R is the correct explanation of A.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion: f(x) = [x] is not differentiable at x = 2.
Reason: f(x) = [x] is not continuous at x = 2.
To understand why the correct answer is option 'A', let's break down the given assertion and reason:
Explanation:
Differentiability:
Differentiability is a property of a function that indicates whether the function has a derivative at a particular point. A function is said to be differentiable at a point if the derivative of the function exists at that point.
Continuity:
Continuity is a property of a function that indicates whether the function is continuous at a particular point. A function is said to be continuous at a point if the function is defined at that point and the limit of the function as x approaches that point exists and is equal to the value of the function at that point.
Assertion:
The assertion states that the function f(x) = [x] is not differentiable at x = 2. The function [x] represents the greatest integer less than or equal to x. Therefore, [2] = 2.
Reason:
The reason states that the function f(x) = [x] is not continuous at x = 2. To determine if this statement is true, we need to evaluate the left-hand limit and the right-hand limit of the function as x approaches 2.
Evaluation:
- Left-hand limit: lim(x->2-) [x] = 1 (greatest integer less than 2 is 1)
- Right-hand limit: lim(x->2+) [x] = 2 (greatest integer less than 2 is 2)
Since the left-hand limit and the right-hand limit are not equal, the limit of the function as x approaches 2 does not exist. Therefore, the function is not continuous at x = 2.
Conclusion:
Both the assertion and the reason are true, and the reason correctly explains why the function f(x) = [x] is not differentiable at x = 2. The lack of continuity at x = 2 prevents the existence of a derivative at that point. Hence, option 'A' is the correct answer.
Reason: f(x) = [x] is not continuous at x = 2.
To understand why the correct answer is option 'A', let's break down the given assertion and reason:
Explanation:
Differentiability:
Differentiability is a property of a function that indicates whether the function has a derivative at a particular point. A function is said to be differentiable at a point if the derivative of the function exists at that point.
Continuity:
Continuity is a property of a function that indicates whether the function is continuous at a particular point. A function is said to be continuous at a point if the function is defined at that point and the limit of the function as x approaches that point exists and is equal to the value of the function at that point.
Assertion:
The assertion states that the function f(x) = [x] is not differentiable at x = 2. The function [x] represents the greatest integer less than or equal to x. Therefore, [2] = 2.
Reason:
The reason states that the function f(x) = [x] is not continuous at x = 2. To determine if this statement is true, we need to evaluate the left-hand limit and the right-hand limit of the function as x approaches 2.
Evaluation:
- Left-hand limit: lim(x->2-) [x] = 1 (greatest integer less than 2 is 1)
- Right-hand limit: lim(x->2+) [x] = 2 (greatest integer less than 2 is 2)
Since the left-hand limit and the right-hand limit are not equal, the limit of the function as x approaches 2 does not exist. Therefore, the function is not continuous at x = 2.
Conclusion:
Both the assertion and the reason are true, and the reason correctly explains why the function f(x) = [x] is not differentiable at x = 2. The lack of continuity at x = 2 prevents the existence of a derivative at that point. Hence, option 'A' is the correct answer.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : f(x) = [x] is not differentiable at x = 2.Reason : f(x) = [x] is not continuous at x = 2.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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