Consider the following statements: (i) When \((0 < x < 1)\), then \((\frac{1}{1+x} < 1 - x + x^2)\) (ii) When \((0 < x < 1)\), then \((\frac{1}{1+x} > 1 - x + x^2)\) (iii) When \((-1 < x < 0)\),…
Question and options
Consider the following statements:
(i) When , then
(ii) When , then
(iii) When , then
(iv) When , then
Then the correct statements are:
(i) When , then
(ii) When , then
(iii) When , then
(iv) When , then
Then the correct statements are:
- (i) and (ii)
- (ii) and (iv)
- (i) and (iv)
- (ii) and (iii)
Answer and explanation
Correct answer: C - (i) and (iv)
(1+x)(1-x+x^2)=1+x^3, so 1-x+x^2=(1+x^3)/(1+x). For 0<x<1, 1+x^3>1 so 1/(1+x) is smaller: (i) true. For -1<x<0, 1+x^3<1 (and 1+x>0) so 1/(1+x) is larger: (iv) true.
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IPMAT Indore
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