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("lim")(xvec0)[(sin(sgn(x)))/((sgn(x)))]...

`("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))],` where`[dot]` denotes the greatest integer function, is equal to (a)0 (b) 1 (c) `-1` (d) does not exist

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")(xvec0)[(sin(sgn(x)))/((sgn(x)))], where[dot] denotes the great...

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  2. Let lim(x->0)([x]^2)/(x^2)=l and lim(x->0)([x^2])/(x^2)=m , where [dot...

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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")(xvec0)(a^(sqrt(x))-a^(1 / sqrt(x)))/(a^...

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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 x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xvecoo)xn is -1 ...

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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),a n dh(x)=-(2(2x+1))/(x^2+x-12),t h e...

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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)i s (a)1/(...

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  13. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  14. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  15. about to only mathematics

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  16. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

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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. evaluate (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underse...

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

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  20. ("lim")(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n-1))i se q u a lto 0 (b) 2...

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