Home
Class 12
MATHS
(lim)(x->0)((1^x+2^x+3^x++n^x)/n)^(1/x)\...

`(lim)_(x->0)((1^x+2^x+3^x++n^x)/n)^(1/x)\ ` is equal to `(n\ !)\ ^n` b. `(n !)^(1//n)` c. `n !` d. `"ln"(n !)`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos

  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

lim_(xrarr0)((1^(x)+2^(x)+3^(x)+…..+n^(x))/(n))^((a)/(x)) equals

lim_(x rarr0)((1^(x)+2^(x)+.........*+n^(x))/(n))^((1)/(x)) is equal

lim_(x rarr0)((1^(x)+2^(x)+3^(x)+...+n^(x))/(n))^((1)/(x))

lim_(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

(lim_(x rarr a)(x^(n)-a^(n))/(x-a) is equal to na^(n)b*na^(n-1) c.nad.1

lim_(x rarr2)((1+x)^(n)-3^(n))/(x-2)=n*3^(n-1)

If (lim)_(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the value of ' a ' is equal to 1/n b. n^2+1 c. (n^2+1)/n d. none

lim_(x->oo)(e^x((2^(x^n))^(1/(e^(x)))-(3^(x^n))^(1/(e^(x)))))/(x^n), n in N, is equal to

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. lim(x->0) sin(x^2)/(ln(cos(2x^2-x)) is equal to

    Text Solution

    |

  2. If f(x)={x^nsin(1/(x^2)),x!=0 0,x=0,(n in I),t h e n ("lim")(xvec0)...

    Text Solution

    |

  3. (lim)(x->0)((1^x+2^x+3^x++n^x)/n)^(1/x)\ is equal to (n\ !)\ ^n b. (n...

    Text Solution

    |

  4. Among (i) ("lim")(xvec0)sec^(-1)(x/(sinx))a n d(i i i)("lim")(xvecoo)s...

    Text Solution

    |

  5. If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n m...

    Text Solution

    |

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

    Text Solution

    |

  7. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

    Text Solution

    |

  8. If ("lim")(xvec0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n m...

    Text Solution

    |

  9. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

    Text Solution

    |

  10. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  11. ABC is an isosceles triangle described in a circle of radius r.If AB=...

    Text Solution

    |

  12. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  13. If f(x) = |1 -x|, then the points where sin^-1 (f |x|) is non-differen...

    Text Solution

    |

  14. Let f(x)=1/(1+e^(1/x))for\ x!=0\ a n d\ f(0)=0 , then f(0^+) does not ...

    Text Solution

    |

  15. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

    Text Solution

    |

  16. In a quadratic equation ax^2 + bx+c= 0 if 'a' and 'c' are of opposite ...

    Text Solution

    |

  17. Let f(x)""=""x|x|""a n d""g(x)""=""s in x Statement 1 : gof is diff...

    Text Solution

    |

  18. Statement 1:(lim)(x->0)sin^(-1){x}\ does not exist (where {.} denot...

    Text Solution

    |

  19. Statement 1: lim(x->0) sqrt(1-cos 2x)/x does not existe . Statement 2...

    Text Solution

    |

  20. Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i ...

    Text Solution

    |