Home
Class 12
MATHS
Evaluate: ("lim")(xvecoo)((a1^( 1/x)+a2^...

Evaluate: `("lim")_(xvecoo)((a_1^( 1/x)+a_2^ (1/x)+ --+a_ n^(1/x))/n)^(n x)`

A

`a_1+a_2+...a_n`

B

`e^(a_1+a_2+..+a_n)`

C

`(a_1+a_2+...+a_n)/(n)`

D

`a_1a_2.......a_n`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|96 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

Evaluate the limit: ("lim")_(xvecoo)((x+2)/(x+1))^(x+3)

Evaluate : lim_(x to 1) (x^(m)-1)/(x^(n)-1)

Evaluate lim_(xto1)(x+x^(2)+…….+x^(n)-n)/(x-1)

Let f(x)=(lim)_(xvecoo)(tan^(-1)(tanx))/(1+((log)_e x)^n),x!=(2n+1)pi/2 then AA1 e ,f(x) is a constant function

If ("lim")_(xvecoo){(x^2+1)/(x+1)-(a x+b)}=0, then find the value of aa n dbdot

Let y = 1 + (a_(1))/(x - a_(1)) + (a_(2) x)/((x - a_(1))(x - a_(2))) + (a_(3) x^(2))/((x - a_(1))(x - a_(2))(x - a_(3))) + … (a_(n) x^(n - 1))/((x - a_(1))(x - a_(2))(x - a_(3))..(x - a_(n))) Find (dy)/(dx)

If a_1,a_2, ,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a_1+a_2++a_(n-1)+2a_n is a_(n-1)+2a_n is b. (n+1)c^(1//n) 2n c^(1//n) (n+1)(2c)^(1//n)

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-1)+...+a_(n-1)x+a_(n)

If 0lta_1lta_2lt....lta_n , then prove that tan^(-1)((a_1x-y) /(x+a_1y))+tan^(-1)((a_2-a_1) /(1+a_2a_1))+tan^(-1)((a_3-a_2)/(1+a_3a_2))+.......+tan^(-1)((a_n-a_(n-1)) /(1+a_n a_(n-1)))+tan^(-1)(1/(a_n))=tan^(-1)(x/y)dot

If a_1,a_2,------ ,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a_1+a_2+---+a_(n-1)...........+2a_n is a. a_(n-1)+2a_n is b. (n+1)c^(1//n) c. 2n c^(1//n) d. (n+1)(2c)^(1//n)

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. The value of lim(x->a) (sinx/sina)^(1/(x-a))=

    Text Solution

    |

  2. Evaluate the following limit: (lim)(x->oo)((x^2+2x+3)/(2x^2+x+5))^((3x...

    Text Solution

    |

  3. Evaluate: ("lim")(xvecoo)((a1^( 1/x)+a2^ (1/x)+ --+a n^(1/x))/n)^(n x)

    Text Solution

    |

  4. The value of lim(xrarr0) ((sinx)/(x))^((sinx)/(x-sinx)), is

    Text Solution

    |

  5. lim(x->1)[(x^3+2x^2+x+1)/(x^2+2x+3)]^((1-cos(x-1))/(x-1)^2)

    Text Solution

    |

  6. The value of lim(xrarr0) (sinx)/(xqrt(x^2)), is

    Text Solution

    |

  7. Let f:R to R be a differentiable function such that f(2)=2. Then, the ...

    Text Solution

    |

  8. Let f''(x) be continuous at x = 0 and f"(0) = 4 then value of lim(x->0...

    Text Solution

    |

  9. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

    Text Solution

    |

  10. Find the values of aa n db in order that ("lim")(xvec0)(x(1+acosx)-bsi...

    Text Solution

    |

  11. If lim(x->a)(f(x)/(g(x))) exists, then

    Text Solution

    |

  12. Let f (2) = 4 f(2) = 4 Then Lt(x to 2) (x f(2) -2 f(x))/(x -2) is

    Text Solution

    |

  13. lim(x->0) 1/x [inty ^a)e^(sin^2t) dt-int(x+y) ^a)e^(sin^2t)dt] is equ...

    Text Solution

    |

  14. lim(xrarr oo) (int(0) ^(2x)xe^(x^(2))dx)/(e^(4x^2))

    Text Solution

    |

  15. Evaluate underset(xto0)lim(3x+|x|)/(7x-5|x|).

    Text Solution

    |

  16. Let alpha, beta (a lt b) be the roots of the equation ax^(2)+bx+c=0. I...

    Text Solution

    |

  17. Given that lim(nto oo) sum(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1...

    Text Solution

    |

  18. ("lim")(xvec0)((1^x+2x+3^x++n^x)/n)^(1//x)i se q u a lto (n !)^n (b)...

    Text Solution

    |

  19. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

    Text Solution

    |

  20. If lim(xrarroo) {ax-(x^2+1)/(x+1)}=b , a finite number, then

    Text Solution

    |