Home
Class 12
MATHS
lim(nto oo)sum(r=1)^(n)r/(n^(2)+n+4) equ...

`lim_(nto oo)sum_(r=1)^(n)r/(n^(2)+n+4)` equals
a. 0
b. 1/3
c. 1/2
d.1

A

(a) `1/4 sin 4+1/15 cos 4-1/16`

B

(b) `1/4 sin 4-1/16cos 4 +1/16`

C

(c) `1/16(1-sin4)`

D

(d) `1/16(1-cos4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • LIMITS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|10 Videos

  • LIMITS

    ARIHANT MATHS|Exercise SOLVED EXAMPLES|1 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|4 Videos

Similar Questions

Explore conceptually related problems

lim_(nto oo)sum_(r=1)^(n)r/(n^(2)+n+4) equals a. 0 b. 1/3 c. 1/2 d.1

The value of lim_(nto oo)(1)/(2) sum_(r-1)^(n) ((r)/(n+r)) is equal to

Lim_(n to 0) sum_(x + 1)^(n) tan^(-1) (1/(2r^2)) equals

The value of lim_(n to oo)(1)/(n).sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) is equal to

Let S be the sum of all possible determinants of order 2 having 0,1,2 and 3 as their elements,. Find the common root alpha of the equations x^(2)+ax+[m+1]=0, x^(2)+bx+[m+4]=0 and x^(2)-cx+[m+15]=0 such that alphagtS wherea+b+c=0 and m=lim_(n to 00)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) and [.] denotes the greates integer function.

Let r^(th) term t _(r) of a series if given by t _(c ) = (r )/(1+r^(2) + r^(4)) . Then lim _(n to oo) sum _(r =1) ^(n) t _(r) is equal to :

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR the value of lim_(xtooo)sum_(r=1)^(n)((4r)f(3r))/(n^(3)) is ……….

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is a. 0 b. -log2 c. 1 d. e

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
  1. lim(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to

    Text Solution

    |

  2. The value of lim(xto0)2/(x^(3))(sin^(-1)x-tan^(-1)x)^(2//x^(3)) equals

    Text Solution

    |

  3. lim(nto oo)sum(r=1)^(n)r/(n^(2)+n+4) equals a. 0 b. 1/3 c. 1/2 d.1

    Text Solution

    |

  4. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10};...

    Text Solution

    |

  5. int(-1)^(2)[([x])/(1+x^(2))]dx, where [.] denotes the greatest integer...

    Text Solution

    |

  6. If alpha and beta are roots of x^(2)-(sqrt(1-cos 2 theta))x+theta=0, w...

    Text Solution

    |

  7. If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim(xto...

    Text Solution

    |

  8. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2ltf(x)lt(x^2|...

    Text Solution

    |

  9. Let f(x) be polynomial of degree 4 with roots 1,2,3,4 and leading coef...

    Text Solution

    |

  10. lim x→π/4 (4sqrt(2)-(cosx+sinx)^5)/(1−sin2x) is equal to

    Text Solution

    |

  11. If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3, the number ...

    Text Solution

    |

  12. Let f(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the...

    Text Solution

    |

  13. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

    Text Solution

    |

  14. Find dy/dx if x^7-e^x=siny

    Text Solution

    |

  15. underset(xto(pi)/(2))(lim)([(x)/(2)])/(log(e)(sinx))([.] denotes great...

    Text Solution

    |

  16. If tn=1/4(n+2)(n+3) for n=1,2,3, , then 1/(t1)+1/(t2)+1/(t3)++1/(t(20...

    Text Solution

    |

  17. If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1, then find the val...

    Text Solution

    |

  18. Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))......

    Text Solution

    |

  19. If f(x)={("sin"[x])/([x]),for[x]!=0, 0,for[x]=0,where [x] denotes the...

    Text Solution

    |

  20. Evaluate: lim(xto2)(x^3-6x^2+11 x-6)/(x^2-6x+8)

    Text Solution

    |