Home
Class 12
MATHS
lim(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)...

`lim_(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)}` =

A

`pi/3`

B

1

C

`(2pi)/3`

D

`pi/6`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos
  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

lim_(n rarr oo) 1/n[sin(pi/(2n))+sin(pi/n)+sin((3pi)/2n)+........+sin(pi/2)] =

lim_(n rarr oo) (1-n^(2))/(sum n)=

lim_(n rarr oo) 5^(((2x)/(x+3)) =

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

lim_(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

The smallest positive integral value of n such that [(1+"sin"pi/8+i"cos"(pi)/8)/(1+"sin"(pi)/8-i"cos"(pi)/8)]^(n) is purely imaginary is n=

lim_(n to oo) [1/(n^2) "sec"^2 1/(n^2) + 2/(n^2) "sec"^(2) 4/(n^2) + …… + 1/n "sec"^(2) 1] equals :

Lim_(nto oo)(3^(n)+4^(n))^((1)/(n))=

underset(n to oo)lim 1/n [ tan pi/(4n) + tan (2pi)/(4n) + tan (3pi)/(4n) + …. + tan(npi)/(4n)] =

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(x rarr 0)"x sin" (1)/(x) is equal to :

    Text Solution

    |

  2. lim(n to oo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

    Text Solution

    |

  3. lim(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)} =

    Text Solution

    |

  4. underset(xtoa)(lim)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x))=

    Text Solution

    |

  5. lim(x rarr oo) (1+2/n)^(2n)=

    Text Solution

    |

  6. If f(9) =9, f^(')(9) = 4, then lim(x rarr 9)(sqrt(f(x))-3)/(sqrtx - 3)...

    Text Solution

    |

  7. If f(x) = {((x^(5)-32)/(x-2), x ne 2),(k, x =2):} is continuous at x =...

    Text Solution

    |

  8. The points of discontinuity of f(x) = tan((pix)/(x+1))

    Text Solution

    |

  9. If the function f(x) = {{:((x^(2)-(a+2)x + a)/(x-2),,x ne 2),(2,,x = 2...

    Text Solution

    |

  10. The value of f(0) so that the function f(x) = (2x-sin^(-1)x)/(2x+tan^(...

    Text Solution

    |

  11. How should we define f(x) = (log(1+ax)-log(1-bx))/x at x = 0 so as to...

    Text Solution

    |

  12. Which of the following is false ?

    Text Solution

    |

  13. If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 th...

    Text Solution

    |

  14. Let f(x) = {((sin pix)/(5x), x ne 0),(k, x =0):} If f(x) is continuous...

    Text Solution

    |

  15. The function f(x)=|x|+(|x|)/(x) is

    Text Solution

    |

  16. If f(x)={((1-cosx)/(x),xne0),(k, x=0):} is continuous at x=0 then k=

    Text Solution

    |

  17. If f(x) = {((sin 5x)/(x^(2)+2x), x ne 0),(k+1/2, x =0):} is continuous...

    Text Solution

    |

  18. Which one of the following is not true always?

    Text Solution

    |

  19. The points of discontinuity of f(x) = tan((pix)/(x+1))

    Text Solution

    |

  20. Let f(x) = {(-2sinx, x le -pi/2),(asinx +b, -pi/2 lt x lt pi/2),(cosx,...

    Text Solution

    |