Home
Class 12
MATHS
If underset(xto0)lim[1+xln(1+b^(2))]^(1/...

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

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

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

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

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 6sin^(2)theta - sin theta = 1 and 0 le theta le pi , what is the value of sin theta ?

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(3)) , then value of theta is

If sin theta = (1)/(2)cos theta , and 0 le theta le (pi)/(2) , the value of (1)/(2)sin theta is

Evaluate underset(xto0)lim(1-cosmx)/(1-cosnx).

If (1-tan theta)(1+tan theta)sec^2 theta+2^(tan^2 theta)=0 then in the interval (-pi/2,pi/2), the value of theta is

If lim_(xto0) (1+ax+bx^(2))^(2//x)=e^(3) , then find the values of a and b.

underset (xto0)lim(10^(x)-2^(x)-5^(x)+1)/(l n (secx)) is equal to

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

    Text Solution

    |

  2. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

    Text Solution

    |

  3. If underset(xto0)lim[1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and ...

    Text Solution

    |

  4. Let f(x) = {{:(x^(2)|"cos"(pi)/(x)|",",x ne 0","x in R),(0",",x = 0):}...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  8. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

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

    Text Solution

    |

  10. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  11. Let f : R rarr R be a function such that f(x+y) = f(x) + f(y), AA x, y...

    Text Solution

    |

  12. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

    Text Solution

    |

  13. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  14. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  15. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  16. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  17. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  18. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  19. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  20. Let alpha,betainR be such that underset(xto0)lim(x^(2)sin(betax))/(alp...

    Text Solution

    |