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`("lim")_(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot]` represents the greatest integer function). `-1` (b) 1 (c) 0 (d) does not exist

A

1

B

2

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto0^(+))lim[(1-e^(x))(sinx)/(|x|)]=underset(xto0^(+))lim[(0^(-))(sinx)/(x)]=[0^(-)]=-1.`
`underset(xto0^(-))lim[(1-e^(x))(sinx)/(|x|)]=underset(xto0^(-))lim[(0^(+))(sinx)/(-x)]=[0^(-)]=-1`
Hence, `underset(xto0)lim[(1-e^(x))(sinx)/(|x|)]=-1.`
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CENGAGE-LIMITS-Exercise (Single)
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  4. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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

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

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

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

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

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

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

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

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

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

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

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