Home
Class 12
MATHS
If underset( x to 0) lim [1+x log (1+b...

If ` underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) theta, b gt 0 and theta in ( - 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

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise SELF ASSESSMENT TEST (TRUE AND FALSE TYPE QUESTIONS) |1 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise SELF ASSESSMENT TEST (FILL IN THE BLANKS) |4 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (5) (MULTIPLE CHOICE QUESTIONS) |12 Videos

  • INVERSE CIRCULAR FUNCTIONS

    ML KHANNA|Exercise Self Assessment Test|25 Videos

  • LINEAR PROGRAMMING

    ML KHANNA|Exercise Self Assessment Test|8 Videos

Similar Questions

Explore conceptually related problems

If lim_( x to 0) [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) theta, b gt 0 and theta in ( - 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 2 sin^2 theta - 5 sin theta + 2 gt 0, theta in (0,2pi)," then" theta in :

If x + iy = (1)/(1-cos theta + 2 i sin theta), theta ne 2n pi, n in I , then maximum value of x is

for theta in [ 0, pi ] , let f( theta) = sin ( cos theta) and g ( theta) = cos ( sin theta ) . Let a = underset( 0 le theta le pi ) (" max") f ( theta) , b= underset(0 le theta le pi )( min) f( theta), c = underset(0 le theta le pi ) ( " max") g( theta) and d= underset( 0 le theta le pi )( min g( theta) . the correct inequalities satisfied by a,b,c,d are

If 0<=theta<=pi and (sin0)/(2)=sqrt(1+sin theta)-sqrt(1-sin theta) then the possible value of tan theta, is -

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)/(2)) , then value of theta is

If x = a (theta + sin theta), y = b (1+ cos theta), then (dy)/(dx)" at "theta = (pi)/(2) is:

ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)
  1. The function f (x) = 1+ |sin x| is

    Text Solution

    |

  2. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

    Text Solution

    |

  3. The following functions are continuous on (0, pi)

    Text Solution

    |

  4. If f (x) = 1/2 x - 1, then on the interval [0, pi]

    Text Solution

    |

  5. If f(x) = 3x-5, then f^(-1) (x)

    Text Solution

    |

  6. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

    Text Solution

    |

  7. Show that the underset(xto2)lim((sqrt(1-cos{2(x-2)}))/(x-2)) doesnot e...

    Text Solution

    |

  8. Let f: R to R be a positive increasing function with lim(x to infty) (...

    Text Solution

    |

  9. If underset(x to infty)lim((x^(2)+x+1)/(x+1)-ax -b)=4 then

    Text Solution

    |

  10. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

    Text Solution

    |

  11. Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f...

    Text Solution

    |

  12. If f: R to R is a function defined by f(x) = [x] cos((2...

    Text Solution

    |

  13. Let L= lim(x to 0)(a- sqrt(a^(2)-x^(2))-x^(2)/4)/x^(4), a gt 0. If L i...

    Text Solution

    |

  14. Let f: R to R be a function such that f(x+y) = f(x) + f(y) AA x, y in...

    Text Solution

    |

  15. If f(x) = {{:(-x-pi/2" , " x le - pi/2),(-cos x" , " -pi/2 lt ...

    Text Solution

    |

  16. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

    Text Solution

    |

  17. Let f be a real valued function defined on the interval [0,infty] by f...

    Text Solution

    |

  18. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  19. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

    Text Solution

    |

  20. Let f(x)={x^2 |cospi/x|, ,x !=0, x in R, x=0 then f is

    Text Solution

    |