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Given that for each a epsilon(0,1),lim(h...

Given that for each `a epsilon(0,1),lim(hto 0^(+)) int_(h)^(1-h)t^(-a)(1-t)^(a-1)dt` exists. Let this limit be `g(a)`. In addition it is given the function `g(a)` is differentiable on`(0,1)`.
The value of `g(1/2)` is a. `(pi)/2` b. `pi` c.`-(pi)/2` d. `0`

A

`pi/2`

B

`pi`

C

`-(pi)/(2)`

D

`0`

Text Solution

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The correct Answer is:
D
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

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  2. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  3. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  4. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

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  5. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

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  6. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  7. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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  8. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  9. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

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  10. The option(s) with the values of aa n dL that satisfy the following eq...

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  11. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  12. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  13. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

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  14. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

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  15. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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  16. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

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  17. Let f:Rto(0,1) be a continuous function. Then, which of the following ...

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  18. Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...

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  19. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...

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  20. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

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