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The value of lim(x rarr0)(int0^(x^2) cos...

The value of `lim_(x rarr0)(int_0^(x^2) cost^2dt)/(x sin x)` is

A

`frac(3)(2)`

B

1

C

-1

D

none of these

Text Solution

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The correct Answer is:
B
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If lim(x rarr 0)(((a-n)nx-tanx)sinnx)/x^2=0, where n is non zero real ...

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  2. lim(x rarrpi/4)(int2^(sec^2x) f(t)dt)/(x^2-pi^2/16)

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  3. The value of lim(x rarr0)(int0^(x^2) cost^2dt)/(x sin x) is

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  4. If f(x)=1/3{f(x+1)+5/(f(x+2)}} and f(x) gt 0 for all x in R, then lim(...

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  5. If phi(x)=lim(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)), then

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  6. Let f(x) = [x^3 - 3] where [.] denotes the greatest integer function T...

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  7. If f(x)={(x[x], 0lexlt2),((x-1)[x], 2lexle3'):}, where [.] denotes the...

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  8. If f(x)={(4, -3ltxlt-1),(5+x, -1lexlt0),(5-x, 0 lexlt2),(x^2+x-3, 2le...

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  9. Let f(x)={((x-4)/(|x-4|)+a, xlt4),(a+b, x=4),((x-4)/(|x-4|)+b,x gt 4)...

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  10. Let f(x)= {(a|x^2-x-2| /(2+x-x^2) , xlt2),(b, x = 2), ((x-[x])/(x-2), ...

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  11. The value of f (0), so that function f(x) = (sqrt(a^2-ax+x^2)-sqrt(a^...

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  12. Let f(x) = |x|-1|, then points where f(x), is not differentiable is/ar...

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  13. Let f be twice differentiable function satisfying f(1) = 1, f(2) = 4, ...

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  14. f(x)= min{1, cosx, 1-sinx}, -pilexlepi then

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  15. Let f : R rarr R be any function. Define g : R rarr R by g(x)=|f(x)| f...

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  16. If f(x) = lim(nrarr infty)(sinx)^(2n) where n in l^+ then f(x) is

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  17. The function f(x)=(sin2x)^(tan^2 2x) is not defined at x=pi/4. The val...

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  18. Let f : R rarr R be a differentiable function having f(2) = 6, f'(2) =...

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  19. The value of lim(xrarr0)frac(1)(x^3) int0^(x) (t log(1+t))/(t^4+4)dt ...

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  20. Let f: RrarrR be such that f (1) = 3 and f' (1) = 6 Then, lim(xrarr0)(...

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