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("lim")(xvec0)(x^asin^b x)/(sin(x^c)),w ...

`("lim")_(xvec0)(x^asin^b x)/(sin(x^c)),w h e r ea , b , c in R ~{0},e xi s t sa n dh a s` non-zero value. Then, `a+c=b` (b) `-1` `0` (d) none of these

A

`a-b+c=0`

B

`a-b-c=0`

C

`a+b-c=0`

D

None of these

Text Solution

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The correct Answer is:
C
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Evaluate underset(xto0)lim(3x+|x|)/(7x-5|x|).

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  2. If [ ] denotes the greatest integer function, lim(x to(pi)/2)(5 sin ...

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  3. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)),w h e r ea , b , c in R ~{0},e ...

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  4. lim(x->0)(2 7^x-9^x-3^x+1)/(sqrt(2)-sqrt(1+cosx))

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  5. Evaluate: lim(xto-1)(log(x^(2)+2x+5)+"cos5"((x+1))/6-"cos"((x+1))/6-lo...

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  6. The value of lim(xto2a)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(sqrt(x^2-4a^2))i...

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  7. Evaluate: lim(xto0)(log(1-3x))/(5^(x)-1)

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  8. int e^x sec e^x dx

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  9. Evaluate: lim(xto0)(log(e^(x)-x))/(1-cosx)

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  10. Evaluate: (lim)(x->e)(logx-1)/(x-e)

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  11. Evaluate: ("lim")(xvec0)((a^x+b^x+c^x)/3);(a , b , c >0)

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  12. Evaluate underset(xto2)limsin(e^(x-2)-1)/(log(x-1))

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  13. The value of lim(xto0)(x cosx-log(1+x))/(x^(2)) is

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  14. If x gt0 and g is bounded function then lim(ntooo)(f(x)e^(nx)+g(x))/(e...

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  15. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  16. If lim(xtooo)(1+a/x+b/(x^(2)))^(2x)=e^2 then values of a and b are

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  17. If lim(xto0)({(a-n)nx-tanx}sin nx)/(x^(2))=0, where n is non zero real...

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  18. Find the values of a and b in order that underset(xto0)lim(x(1+acosx...

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  19. Evaluate underset(xto0)lim(sin[cosx])/(1+[cosx]) ([.] denotes the grea...

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  20. lim (xto (pi)/(3 )) (sin ((pi)/(3)-x))/( 2 cos x-1) is equal to:

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