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Consider the following statements:
1. f(x) = In x is an increasing function on (0, ∞).
2. f(x) = ex - x (In x) is an increasing function on (1, ∞).
1. f(x) = In x is an increasing function on (0, ∞).
2. f(x) = ex - x (In x) is an increasing function on (1, ∞).
Q. Which of the above statements is/are correct ?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements:1. f(x) = In x is an increasing func...
f(x) = logx
Clearly f(x) is increasing on (0,∞)
f(x) = ex-xlogx
f '(x) = ex - (log x +1)
Clearly f(x) is increasing on (0,∞)
f(x) = ex-xlogx
f '(x) = ex - (log x +1)
From the figure it is clear that f'(x) > 0 on (1, ∞).
So both statements (1) & (2) are correct.
So both statements (1) & (2) are correct.
Most Upvoted Answer
Consider the following statements:1. f(x) = In x is an increasing func...
∞)
2. f(x) = x^2 is a decreasing function on (-∞, 0)
Which of the statements is true?
1. The first statement is true. The natural logarithm function, ln(x), is increasing on the interval (0, ∞). This means that as x increases, the value of ln(x) also increases.
2. The second statement is false. The function f(x) = x^2 is actually an increasing function on the interval (-∞, 0). As x decreases, the value of x^2 also decreases. Therefore, the function is not decreasing on this interval.
2. f(x) = x^2 is a decreasing function on (-∞, 0)
Which of the statements is true?
1. The first statement is true. The natural logarithm function, ln(x), is increasing on the interval (0, ∞). This means that as x increases, the value of ln(x) also increases.
2. The second statement is false. The function f(x) = x^2 is actually an increasing function on the interval (-∞, 0). As x decreases, the value of x^2 also decreases. Therefore, the function is not decreasing on this interval.
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Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer?.
Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer?.
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