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Lim(hto0)(int(a)^(x+h)ln^(2)tdt-inta^(x)...

`Lim_(hto0)(int_(a)^(x+h)ln^(2)tdt-int_a^(x)ln^(2)tdt)/(h)` equals to :

A

0

B

`ln^(2)x`

C

`(2lnx)/(x)`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. f(x) = int(x)^(x^(2))(e^(t))/(t)dt, then f'(t) is equal to :

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  2. f(x) = underset(0)overset(x)(t-1)(t-2)^(2)(t-4)^(5) dt (xgt0) then num...

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  3. Lim(hto0)(int(a)^(x+h)ln^(2)tdt-inta^(x)ln^(2)tdt)/(h) equals to :

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  4. The value of the function f(x) = 1+x+int(1)^(x)(ln^(2)t+2lnt)dt, where...

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  5. If int(a)^(y)cost^(2)dt = int(a)^(x^(2))(sint)/(t) dt, then the value ...

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  6. If int(sinx)^(1)t^(2) (f(t)) dt = (1-sinx), then f ((1)/(sqrt(3))) is

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  7. The value of lim(a rarr oo)(1)/(a^(2))int(0)^(a)ln(1+e^(x))dx equals

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  8. f(x) = underset(1)overset(sinxcosy)int(y^(2)+y+1)dy, then

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  9. int(0)^(pi//2) sin^(4)xcos^(3)dx is equal to :

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  10. int(0)^(1)x^(2)(1-x)^(3)dx is equal to

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  11. Let I = int(1)^(3)sqrt(x^(4)+x^(2)), dx then

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  12. I=int0^(2pi) e^(sin^2x+sinx+1)dx then

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  13. Let f"'(x)>=0 ,f'(x)> 0, f(0) =3 & f(x) is defined in [-2, 2].If f(x) ...

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  14. Let mean value of f(x) = 1/(x+c) over interval (0,2) is 1/2 ln 3 then...

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  15. lim(nrarr0) sum(r=1)^(n) ((r^(3))/(r^(4)+n^(4))) equals to :

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  16. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

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  17. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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  18. lim(nrarroo) [sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))/(n)pi] i...

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  19. Let I(n) = int(0)^(1)(1-x^(3))^(n)dx, (nin N) then

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  20. The area bounded by the x-axis and the curve y = 4x - x^2 - 3 is

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