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lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (wh...

`lim_(xto0) [(1-e^(x))(sinx)/(|x|)]` is (where `[.]` represents the greatest integer function )

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 PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
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  4. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  7. The value of lim(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x))...

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  9. lim(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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

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  14. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

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  15. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

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  18. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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