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The set of all x for which ln (1 + x) ≤ x is equal to
- a)x > 0
- b)x>–1
- c)–1<x<0
- d)Null set
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The set of all x for whichln (1 + x) ≤ x is equal toa)x > 0b)x&g...
f(x) = ln(1+x) - x ≤ 0
f(x) = ln(1+x) - x
f’(x) = 1/(1+x) - 1
= (1 - 1 - x)/(1+x)
= -x/(1+x)
f’(x) ≤ 0
-x/(1+x) ≤ 0
0 ≤ x /(1+x)
for(x = 2) (-2)/(1-2)
= 2 > 0, therefore x > - 1
f(x) = ln(1+x) - x
f’(x) = 1/(1+x) - 1
= (1 - 1 - x)/(1+x)
= -x/(1+x)
f’(x) ≤ 0
-x/(1+x) ≤ 0
0 ≤ x /(1+x)
for(x = 2) (-2)/(1-2)
= 2 > 0, therefore x > - 1
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Community Answer
The set of all x for whichln (1 + x) ≤ x is equal toa)x > 0b)x&g...
f(x) = ln(1+x) - x ≤ 0
f(x) = ln(1+x) - x
f’(x) = 1/(1+x) - 1
= (1 - 1 - x)/(1+x)
= -x/(1+x)
f’(x) ≤ 0
-x/(1+x) ≤ 0
0 ≤ x /(1+x)
for(x = 2) (-2)/(1-2)
= 2 > 0, therefore x > - 1
f(x) = ln(1+x) - x
f’(x) = 1/(1+x) - 1
= (1 - 1 - x)/(1+x)
= -x/(1+x)
f’(x) ≤ 0
-x/(1+x) ≤ 0
0 ≤ x /(1+x)
for(x = 2) (-2)/(1-2)
= 2 > 0, therefore x > - 1
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The set of all x for whichln (1 + x) ≤ x is equal toa)x > 0b)x>–1c)–1<x<0d)Null setCorrect answer is option 'B'. Can you explain this answer? for EmSAT Achieve 2026 is part of EmSAT Achieve preparation. The Question and answers have been prepared according to the EmSAT Achieve exam syllabus. Information about The set of all x for whichln (1 + x) ≤ x is equal toa)x > 0b)x>–1c)–1<x<0d)Null setCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for EmSAT Achieve 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set of all x for whichln (1 + x) ≤ x is equal toa)x > 0b)x>–1c)–1<x<0d)Null setCorrect answer is option 'B'. Can you explain this answer?.
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