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Let f(x) =int-1^x e^(t^2) dt and h(x)=f(...

Let `f(x) =int_-1^x e^(t^2) dt and h(x)=f(1+g(x)),` where `g (x)` is defined for all `x, g'(x)` exists for all `x, and g(x) < 0 for x > 0.` If `h'(1)=e and g'(1)= 1,` then the possible values which `g(1)` can take

A

0

B

`-1`

C

`-2`

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
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  2. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

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  3. Let f(x) =int-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is define...

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  4. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

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  5. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4)) and g be the inverse of f. ...

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  6. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

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  7. Let f be a positive function. Let I(1)=int(1-k)^(k)x f[x(1-x)]dx , I(...

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  8. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

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  9. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx where a is positive r...

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  10. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

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  11. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

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  12. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

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  13. lim(n rarr infty) sum(k=1)^(n) (k)/(n^(2)+k^(2)),x gt 0 is equal to

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  14. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

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  15. Evaluate the definite integral: int0^1((xdx)/(1+x))

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  16. The value of int (0)^(infty)e^-(a^(2)x) dx is equal to

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  17. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

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  18. If 2f (x) +f (-x)=(1)/(x) sin (x-(1)/(x)), then the value of int(1//e...

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  19. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

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  20. If f(x) is differentiable function and (f(x).g(x)) is differentiable a...

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