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Let `f:R to R` be a differentiable function such that `f(2)=2`. Then, the value of `lim_(xrarr2) int_(2)^(f(x))(4t^3)/(x-2) dt`, is

A

`6f'(2)`

B

`12 f'(2)`

C

`32f'(2)`

D

none of these

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. lim(x->1)[(x^3+2x^2+x+1)/(x^2+2x+3)]^((1-cos(x-1))/(x-1)^2)

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  2. The value of lim(xrarr0) (sinx)/(xqrt(x^2)), is

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  3. Let f:R to R be a differentiable function such that f(2)=2. Then, the ...

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  4. Let f''(x) be continuous at x = 0 and f"(0) = 4 then value of lim(x->0...

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  5. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

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  6. Find the values of aa n db in order that ("lim")(xvec0)(x(1+acosx)-bsi...

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  7. If lim(x->a)(f(x)/(g(x))) exists, then

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  8. Let f (2) = 4 f(2) = 4 Then Lt(x to 2) (x f(2) -2 f(x))/(x -2) is

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  9. lim(x->0) 1/x [inty ^a)e^(sin^2t) dt-int(x+y) ^a)e^(sin^2t)dt] is equ...

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  10. lim(xrarr oo) (int(0) ^(2x)xe^(x^(2))dx)/(e^(4x^2))

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  11. Evaluate underset(xto0)lim(3x+|x|)/(7x-5|x|).

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  12. Let alpha, beta (a lt b) be the roots of the equation ax^(2)+bx+c=0. I...

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  13. Given that lim(nto oo) sum(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1...

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  14. ("lim")(xvec0)((1^x+2x+3^x++n^x)/n)^(1//x)i se q u a lto (n !)^n (b)...

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  15. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

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  16. If lim(xrarroo) {ax-(x^2+1)/(x+1)}=b , a finite number, then

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  17. If f(1) =g(1)=2, then lim(xrarr1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-...

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  18. Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluat...

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  19. Evaluate : ("lim")(xvecpi/4)(1-cot^3x)/(2-cotx-cot^3x)

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  20. lim(xto0) (1)/(x^12){1-cos (x^2/2)-cos (x^4/4)+cos (x^2/2) cos (x^4/4)...

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