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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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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. The value of lim(x rarr 0) (sqrt((1)/(2) (1-cos 2x)))/(x) is :

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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 0) (sin nx[(a-n)nx - tan x])/(x^(2)) = 0, where n is non-ze...

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  5. Let f(2)=4 and f'(2)=4. Then lim(xto2)(xf(2)-2f(x))/(x-2) is given b...

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  6. lim(x rarr oo) (logx^(n)-[x])/([x]), where n in N and [.] denotes the ...

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  7. Let f(a) = g(a) = k and their n^(th) order derivatives exist and are n...

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  8. Let f:R to R be a positive increasing function with lim(x to oo) (f(3x...

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  9. lim(x rarr 0) x^(2). sin (pi/x) is

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  10. If 0 lt x lt y, then lim(n rarroo)(y^(n)+x^(n))^(1/n) is equal to

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  11. The value of lim(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=

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  12. If f(x) = {((sin(1+[x]))/([x]), for [x] ne 0),(0, for [x] = 0):} , wh...

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  13. If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R, then lim(...

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  14. lim(x rarr 0) ((1-e^(x))sin x)/(x^(2)+x^(3)) =

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  15. lim(x rarr 0) (sqrt(1+x)-1)/x =

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  16. If f(x) = [((sin [x])/([x]), [x] ne 0),(0, [x] = 0)], then lim(x rarr ...

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  17. The value of lim(x rarr k^(-)) x -[x], where k is an integer, is

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  18. The value of lim(x rarr 0) (1-cos(1-cosx))/(x^(4)) is

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  19. lim(x rarr 3)[x] =

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  20. lim(x rarr 1) (x^(8)-2x+1)/(x^(4)-2x+1) =

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