Home
Class 12
MATHS
I(n)=int(0)^(pi//4)tan^(n)xdx, then lim(...

`I_(n)=int_(0)^(pi//4)tan^(n)xdx`, then `lim_(n to oo)n[I_(n)+I_(n+2)]` equals :

A

1

B

2

C

`pi//4`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 1|57 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

l_(n)=int_(0)^(pi//4)tan^(n)xdx , then lim_(nto oo)n[l_(n)+l_(n-2)] equals

If l_(n)=int_(0)^(pi//4) tan^(n)x dx, n in N "then" I_(n+2)+I_(n) equals

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

lim_(n to oo)(n!)/((n+1)!-n!)

If I_(n)=overset(pi//4)underset(0)int tan ^(n) x dx, lim_(n to oo) n(I_(n+1)+I_(n-1)) equals

If I_(n)=int_(0)^(pi//4) tan^(n)theta d theta , then I_(8)+I_(6) equals

If I_(n)=int_(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I_(n)+I_(n-2)=1/(n+1) (b) I_(n)+I_(n-2)=1/(n-1) (c) I_(2)+I_(4),I_(6),……. are in H.P. (d) 1/(2(n+1))ltI_(n)lt1/(2(n-1))

I_n = int_0^(pi/4) tan^n x dx , then the value of n(l_(n-1) + I_(n+1)) is

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

Let I_(n)=int_(0)^(pi//4) tan^(n)x dx . Statement-1: (1)/(n+1)lt 2I_(n) lt (1)/(n-1) for all n=2,3,4,….. Statement-2: I_(n)+I_(n-2)=(1)/(n-1) ,n=3,4,5,…...

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

    Text Solution

    |

  2. The value of integral int(1)^(e) (log x)^(3)dx , is

    Text Solution

    |

  3. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

    Text Solution

    |

  4. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

    Text Solution

    |

  5. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

    Text Solution

    |

  6. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

    Text Solution

    |

  7. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

    Text Solution

    |

  8. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

    Text Solution

    |

  9. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

    Text Solution

    |

  10. Let I= int(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral ...

    Text Solution

    |

  11. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  12. int(pi)^(10n) |sin x|dx is equla to

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If int(0)^(oo)e^(-ax)dx=(1)/(a)," then "int(0)^(oo)x^(n)e^(-ax)dx is

    Text Solution

    |

  15. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

    Text Solution

    |

  16. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

    Text Solution

    |

  17. If I(m,n)= int(0)^(1) x^(m) (ln x)^(n)dx then I(m,n) is also equal to

    Text Solution

    |

  18. lim(n->oo)(1^(99)+2^(99)+3^(99)+.......n^(99))/(n^(100))=

    Text Solution

    |

  19. I(n)=int(0)^(pi//4)tan^(n)xdx, then lim(n to oo)n[I(n)+I(n+2)] equals ...

    Text Solution

    |

  20. Let int(0)^(a)f(x)dx = lambda and int(0)^(a)f(2a-x)dx=mu. Then int(0)^...

    Text Solution

    |