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The value of lim(x rarr 0) (int(0)^(x^(2...

The value of `lim_(x rarr 0) (int_(0)^(x^(2))cos t^(2)dt)/(x sin x)` is :

A

`(3)/(2)`

B

1

C

-1

D

None of these

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

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

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  4. lim(x rarr oo) (int(0)^(2x) xe^(2)dx)/(e^(4x^(2))) equals :

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  5. lim(x rarr 2) (sqrt(x-2) + sqrt(x) - sqrt(2))/(sqrt(x^(2) - 4)) is equ...

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  6. lim(x rarr 0) (x sqrt(y^(2) - (y - x)^(2)))/((sqrt(8xy - 4x^(2)) + sqr...

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  7. If S(n) = (1)/(1.4)+(1)/(4.7) + (1)/(7.10) +……. to n terms, then lim(n...

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  8. Let the rth term, t(r), of a series is given by : t(r) = (r)/(1+r^(2) ...

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  9. Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then :...

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  10. Let {x} denote the fractional part of xlim Then lim(X rarr 0) ({x})/(t...

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  11. lim(n rarr oo) [(1)/(1-n^(4))+(8)/(1-n^(4))+…...+(n^(3))/(1-n^(4))] eq...

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  12. lim(x rarr pi//3) (2 sin (x-pi//3))/(1-2 cos x) equals :

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  13. Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} The...

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  14. lim(x rarr 0) (tan [e^(2)]x^(2)-tan[-e^(2)]x^(2))/(sin^(2)x) equals :

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  15. If lim(x rarr 0) (1+px)^(q//x) = e^(4), where p, q, in N, then :

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  16. Let f(x) = 3x^(10) - 7x^(8) + 5x^(6) - 21x^(3) + 3x^(2) - 7. Then lim(...

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  17. Let f(x) = lt x gt^("*"), where lt x gt^("*") is the distance from x t...

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

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  19. If the function f(x) = [((cos x)^(1//x),x ne 0),(k,x = 0):} is continu...

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  20. Let f(x) = |x| "cos" (1)/(x) + 15x^(2), x ne 0, = k, x = 0, then f(x...

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