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("lim")(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x...

`("lim")_(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x^2)-pi)i se q u a lto` 1 (b) `-1` (c) `1/2` (d) `-1/2`

A

`e^((1-e))`

B

`e^(((1-e)/e))`

C

`e^(((e)/(1-e)))`

D

`e^((1+e)/(e))`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xtooo)lim(e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi)=underset(t to0^(+))lim(e^(t^(2))-1)/(2cot^(-1)t^(2)-pi)`
`=underset(t to0^(+))lim(e^(t^(2))-1)/(-2tant^(2))`
`=underset(t to0^(+))lim-(1)/(2)(e^(t^(2))-1)/(t^(2)(tant^(2))/(t^(2)))=-(1)/(2)`
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  2. ("lim")(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c)...

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  3. ("lim")(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x^2)-pi)i se q u a lto 1 (b) -...

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

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

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

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

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

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

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

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

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

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

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

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

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