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lim(xto0) [(sin(sgn(x)))/((sgn(x)))], wh...

`lim_(xto0) [(sin(sgn(x)))/((sgn(x)))],` where `[.]` denotes the greatest integer function, is equal to

A

`^(2n)p_(n)`

B

`^(2n)C_(n)`

C

`(2n)!`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto0^(+))lim[(sin(sgnx))/(sgn(x))]=underset(xto0^(+))lim[(sin1)/(1)]=0`
`underset(xto0^(-))lim[(sin(sgnx))/(sgn(x))]`
`=underset(xto0^(-))lim[sin(-1)/(-1)]`
`=underset(xto0^(-))lim[sin1]`
Hence, the given limit is 0.
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xto0) [(sin(sgn(x)))/((sgn(x)))], where [.] denotes the greatest i...

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  2. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

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  3. lim(xto1) [cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the greate...

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  4. The value of the limit lim(xto0) (a^(sqrt(x))-a^(1//sqrt(x)))/(a^(sqrt...

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  5. If lim(xtoa) {(f(x))/(g(x))} exists, then

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  6. ("lim")(xvec1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional ...

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  7. If x(1)=3 and x(n+1)=sqrt(2+x(n))" ",nge1, then lim(ntooo) x(n)is

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  8. lim(xto0^(+)) (sum(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where nin...

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  9. lim(xtooo) (sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1)is equal to

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  10. If f(x)=(2)/(x-3),g(x)=(x-3)/(x+4)," and "h(x)=-(2(2x+1))/(x^(2)+x-12)...

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  11. The value of lim(xto pi) (1+cos^(3)x)/(sin^(2)x)" is "

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  12. The value of lim(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

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  13. The value of lim(xto2) (2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))" is "

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  14. The value of lim(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2...

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  15. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

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  16. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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  17. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

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  18. Among (i) lim(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim(xtooo) sec^(-...

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  19. lim(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

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  20. lim(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

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