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माना कि सभी x gt 0 के लिए है f(x) = {:(...

माना कि सभी `x gt 0` के लिए है `f(x) = {:(lim),(n rarroo):}((n^(n)(x+n)(x+n/2)....(x+n/n))/(n!(x^2+n^2)(x^2+n^2/4)...(x^2+n^2/n^2)))^(x/n)` है | तब

A

` f(( 1)/(2)) ge f(1)`

B

` f((1)/(3)) le f((2)/(3))`

C

` f ' (2)le 0`

D

` (f'(3))/( f(3)) ge ( f'(2))/( f(2))`

लिखित उत्तर

Verified by Experts

The correct Answer is:
B, C
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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -3 (SECTION -A (JEE ADVANCED Previous Year.s Questions ) )

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  5. माना कि सभी x in-((pi)/2,(pi)/2) f(x) = 7 tan^(8) x + 7tan^(6)x-3tan^(...

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  6. माना कि सभी x in R के लिए, f'(x) = (192x^3)/(2+sin^(4)pix),f(1/2)=0 ...

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  7. निम्नलिखित में से a और L के कौन सा (से) मान समीकरण ( underset( 0)ov...

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  8. underset( - (pi)/(2)) overset( (pi)/(2)) int ( x^(2) cos x )/( 1+e^(x...

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  9. माना कि सभी x gt 0 के लिए है f(x) = {:(lim),(n rarroo):}((n^(n)(x+n)(...

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  10. underset(0)overset(1)int (x)/(x^(2)+1) dx मान ज्ञात कीजिएः

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  11. यदि g(x) = underset( sin x) overset( sin 2x ) int sin ^(-1) (t) dt...

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  12. माना की f: R to (0,1) एक सतत फलन ( continuous functions ) है|तब निम...

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  13. मानाकि f:R rarr R इस प्रकार का अवकलनीय फलन है कि f(0) = 0 , f((pi)/2)...

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  14. sqrt(2) int (sin x dx)/(sin (x-(pi)/(4))) बराबर है

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  15. यदि समाकल int ( 5 tan x)/( tan x- 2) dx = x+aln | sin x - 2 cos x |...

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  16. यदि int f(x) dx= psi (x) , है, तो int x^(5) f( x^(3)) dx बराबर ह...

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  17. int ( 1+ x - (1)/(x)) e^(x+( 1)/(x)) dx बराबर है।

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  18. समाकल int ( dx)/( x^(2) (x^(4) + 1) ^((3)/(4))) का मान है

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  19. समाकल int ( 2x^(12) +5x^(9))/( (x^(5)+x^(3) +1) ^(3)) dx बराबर है

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  20. माना है In = int tan^(n) x dx, ( n gt 1) | यदि I(4) +I(6) = a tan ^(5...

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