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If f(x)=x sin(1/x), x!=0 then lim(x->0)f...

If `f(x)=x sin(1/x), x!=0` then `lim_(x->0)f(x)=` a. 1 b . -1 c. 0 d. does not exist

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`lim_(x->0)f(x)=lim_(x->0)x sin(1/x), x!=0`
L.H.L= `lim_(x->0^-)f(x)=lim_(x->0^-)x sin(1/x)`
Here `x to 0^-` mean `x=0-h`, and `h to 0`
Then
`=lim_(h to 0) f(0-h)`
`=lim_(h to 0) -h sin(1/(-h))`
`=0`
R.H.L= `lim_(x->0^+)f(x)=lim_(x->0^+)x sin(1/x)`
...
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RD SHARMA-LIMITS-All Questions
  1. lim(n->oo)(1^2+2^2+3^2++n^2)/(n^3) is equal to a. 1 b . c. 1/3 d. 0

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  2. lim(x->0)(sin2x)/x is equal to a. 1 b . 1/2 c. 2 d. 0

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  3. If f(x)=x sin(1/x), x!=0 then lim(x->0)f(x)= a. 1 b . -1 c. 0 d. does...

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  4. lim(x->0)(1-cos2x)/x is a. 1 b . 2 c. 4 d. 0

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  5. lim(x->0)x/(tanx) is a. 1 b . 0 c. 4 d. not defined

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  6. lim(x->oo)(sinx)/x equals a. 1 b . 0 c. oo d. does not exist

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  7. lim(x->0)(sinx)/x

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  8. lim(x->a)(x^n-a^n)/(x-a) is equal to a.n a^n b . n a^(n-1) c. n a ...

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  9. lim(x->oo)(sqrt(x^2-1))/(2x+1) is equal to a.0 b . -1 c. 1//2 d. ...

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  10. Evaluate the limit: ("lim")(hvec0)[1/(h8+h3)-1/(2h)]

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  11. (lim)(x->1)(sinpix)/(x-1) is equal to -p c. -1/pi d. 1/pi

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  12. (lim)(x->0)(sqrt+x)-1)/x is equal to a. 1 b . 0 c. 2 d. 1/2

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  13. If f(x)={xsin1/x ,\ x!=0 0,\ \ \ \ \ \ \ \ \ \ x=0 , then lim(x->0)f...

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  14. (lim)(n->oo/((n+1)!+n !) is equal to a. 1 b . 0 c. 2 d. 1/2

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  15. lim(x->oo)a^xsin(b/(a^x)),\ a , b >1 is equal to a.b b . a c. a(log...

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  16. lim(theta->pi//2)(1-sintheta)/((pi//2-theta)costheta) is equal to a. 1...

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  17. The value of lim(x->pi//2)(s e c x-t a n x) is a. 1 b . 0 c. 2 d. -1

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  18. The value of lim(x->oo)(n !)/((n+1)!-(n)!) is a. 1 b . -1 c. 0 d. none...

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  19. The value of lim(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!) is a. 1 b . -1...

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  20. The value of lim(n->oo){(1+2+3++n)/(n+2)-n/2}\ is a. 1 b . -1 c. 1/2 ...

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