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("lim")(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^...

`("lim")_(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s` `e^((1-e))` (b) `e^(((1-e)/e))` (c) `e^((e/(1-e)))` (d) `e^(((1+e)/e))`

A

limit does not exist when `a=pi//6`

B

`L=-1` when `a=pi`

C

`L=1` when `a=pi//2`

D

`L=1` when `a=0`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xtooo)lim[((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x)=e^(underset(xtooo)lim[((e)/(1-e))((1)/(e)-(x)/(1+x))-1]x)`
`=e^(underset(xtooo)lim[(1)/(1-e)-(e)/(1-e)(x)/(1+x)-1]x)`
`=e^(underset(xtooo)lim[(e)/(1-e)-(e)/(1-e)(x)/(1+x)]x)`
`=e^(underset(xtooo)lim(e)/(1-e)[1-(x)/(1+x)]x)`
`=e^((e)/(1-e)underset(xtooo)lim(x)/(1+x))`
`=e^((e)/(1-e)underset(xtooo)lim(1)/(1+(1)/(x)))`
`=e^((e)/(1-e))`
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CENGAGE-LIMITS-Exercise (Single)
  1. ("lim")(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2(1/(m2...

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  2. The value of lim(ntooo) (1)/(n)[e^(1/n)+e^(2/n)+...+e] is

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  3. The value of lim(ntooo) [1/n+2] is

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  4. ("lim")(xvec0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)= -1 (b) 1 ...

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  5. The value of lim(xto0) (2^(3x)-3^(2x))/x is

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  6. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

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  7. The value of lim(ntooo) [(1+2+3+...+n)/n^2] is

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  8. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

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  9. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  10. ("lim")(xto0)((1+tanx)/(1+sinx))^(cos e cx)i se q u a l t o (a)e (b)...

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  11. The value of lim(xto1) (2-x)^(tan((pix)/(2))) is

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  12. The value of ("lim")(xvecoo)(cos"x"/"m")^("m") is 1 (b) e (c) e^(-1...

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  13. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

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  14. ("lim")(nvecoo)"{"(n/(n+1))^(alpha)+sin(1/n)]^n(when alpha in Q) is e...

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  15. ("lim")(xvecoo)[(e/(1-e))(1/e-x/(1+x))]^xi s e^((1-e)) (b) e^(((1-e)...

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  16. ("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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  17. Ifp > q >0a n dp r<-1<q r , then find the value of tan^(-1)(p-q)/(1+p ...

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  18. ("lim")(xvecoo)(x(log"x")^3)/(1+x+x^2)e q u a l 0 (b) -1 (c) 1 ...

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  19. ("lim")(xvecoo)(cot^(-1)(x^(-a)(log)a x)/(sec^(-1)(a^x(log)x a),(a >1)...

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  20. The value of lim(ntooo)(e^(n))/((1+(1)/(n))^(n^(2)))is

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