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The value of lim(xrarr0) ((sinx)/(x))^((...

The value of `lim_(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx))`, is

A

`e^-1`

B

e

C

`1`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. Evaluate the following limit: (lim)(x->oo)((x^2+2x+3)/(2x^2+x+5))^((3x...

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  2. Evaluate: ("lim")(xvecoo)((a1^( 1/x)+a2^ (1/x)+ --+a n^(1/x))/n)^(n x)

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  3. The value of lim(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx)), is

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  4. lim(x->1)[(x^3+2x^2+x+1)/(x^2+2x+3)]^((1-cos(x-1))/(x-1)^2)

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

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

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

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

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

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

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  11. 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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  12. 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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  13. lim(xrarr oo) (int(0) ^(2x)xe^(x^(2))dx)/(e^(4x^2))

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

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

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

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  17. ("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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  18. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

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

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  20. 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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