Home
Class 12
MATHS
If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2...

If `("lim")_(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in (-pi,pi],` then the value of `theta` is `+-pi/4` (b) `+-pi/3` (c) `+-pi/6` (d) `+-pi/2`

A

`+-(pi)/4`

B

`+-(pi)/3`

C

`+-(pi)/6`

D

`+-(pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|9 Videos
  • LIMITS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|5 Videos
  • LIMITS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|26 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos
  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0 ,where theta in (-pi,pi], then the value of theta is (a) +-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2

If lim_(xto0) [1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and "thetain(-pi,pi], then the value of theta is

Find ("lim")_(xvec0){tan(pi/4+x)}^(1//x)

If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi is pi/6 (b) pi (c) 0 (d) pi/4

If (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If theta=sin^(-1){sin (-600^(o) ) } , then one of the possible values of theta is pi/3 (b) pi/2 (c) (2pi)/3 (d) (-2pi)/3

If tan^(-1)(cottheta)=2\ theta , then theta= (a) +-pi/3 (b) +-pi/4 (c) +-pi/6 (d) none of these

If tanA=a/(a+1) and tanB=1/(2a+1) then the value of A+B is: (a). 0 (b). pi/2 (c). pi/3 (d). pi/4

The value of int_0^(pi/2) (dx)/(1+tan^3 x) is (a) 0 (b) 1 (c) pi/2 (d) pi

Period of sin^2 theta is(A) pi^2 (B) pi (C) 2pi (D) pi/2

ARIHANT MATHS ENGLISH-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

    Text Solution

    |

  4. The largets value of non negative integer for which lim(x->1){(-a x+si...

    Text Solution

    |

  5. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

    Text Solution

    |

  6. underset(xto(pi)/(2))lim(cotx-cosx)/((pi-2x)^(3)) equals

    Text Solution

    |

  7. Let p=underset(xto0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x)). Then log(e)p...

    Text Solution

    |

  8. lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

    Text Solution

    |

  9. underset(xto0)lim(sin(picos^(2)x))/(x^(2)) is equal to

    Text Solution

    |

  10. lim(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

    Text Solution

    |

  11. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  12. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  13. If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...

    Text Solution

    |

  14. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)...

    Text Solution

    |

  15. lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and ...

    Text Solution

    |

  16. lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...

    Text Solution

    |

  17. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

    Text Solution

    |

  18. Let f: R->R be such that f(1)=3 and f^(prime)(1)=6. Then lim(x->0)((f...

    Text Solution

    |

  19. lim(x to oo) ((x-3)/(x+2)) is equal to :

    Text Solution

    |