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lim(h rarr 0) ([2 sqrt(3) sin ((pi)/(6) ...

`lim_(h rarr 0) ([2 sqrt(3) sin ((pi)/(6) + h) - cos ((pi)/(6) + h)])/(sqrt(3) h (sqrt(3) cos h - sin h))` is :

A

`2//3`

B

`4//3`

C

`-2 sqrt(3)`

D

`- 4//3`

Text Solution

Verified by Experts

The correct Answer is:
B
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MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
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  2. lim(x rarr oo) ((2 + x)^(40) (4 + x)^(5))/((2-x)^(45)) is :

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  3. lim(h rarr 0) ([2 sqrt(3) sin ((pi)/(6) + h) - cos ((pi)/(6) + h)])/(s...

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  4. lim(x rarr 0) phi (x) = a^(3), a ne 0, then lim(x rarr 0) phi ((x)/(a)...

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  5. lim(x rarr 2^(+)) (([x]^(3))/(3) - [(x)/(3)]^(3)) equals :

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  6. Let f(x) = x (-1)^([1//x]), x ne 0, where [x] denotes the greatest int...

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  7. lim(h rarr 0) (tan (a + 2h) - 2 tan (a + h) + tan a)/(h^(2)) is :

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  9. lim(n rarr oo) ((2)/(3) + ((2)/(3))^(2) + ((2)/(3))^(3) + ……. + ((2)/(...

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  10. lim(x rarr oo) (e^(x^(2)) - cos x)/(x^(2)) is equal to :

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  11. lim(x rarr 0) (log (1 + x + x^(2))+ log (1 - x - x^(2)))/(sec x - cos ...

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  12. The value of lim(n rarr oo) cos ((x)/(2)) cos ((x)/(4))cos ((x)/(8))…....

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  13. lim(x rarr 0) (log(sec x//2) cos x)/(log(sec x)cos x//2) is equal to :

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  14. The value of lim(x rarr 1) ((x^(3) + 2x^(2) + x + 1)/(x^(2) + 2x + 3))...

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  15. If f(x) = (2)/(x-3), g(x) = (x-3)/(x+4) and h (x) = (-2(2x + 1))/(x^(2...

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  16. lim(x rarr oo) ( sqrt(x + sqrt(x + sqrt(x))) - sqrt(x)) is equal to :

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  17. The value of lim(x rarr oo) {(x^(2)sin ((1)/(x))-x)/(1-|x|)} is :

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  18. lim(x rarr 0) [int(y)^(a) e^(sin^(2)t) dt - int(x + y)^(a) e^(sin^(2)t...

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  19. If sum(r = 1)^(k) cos^(-1) beta r = (kpi)/(2), "for any k" ge 1 and A ...

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  20. The value of lim(x rarr 0) (int(0)^(x^(2))cos t^(2)dt)/(x sin x) is :

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