Home
Class 12
MATHS
On the interval (0,(pi)/2) the function ...

On the interval `(0,(pi)/2)` the function `log sinx` is

A

increasing

B

decreasing

C

neither increasing nor decreasing

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A

Let `f(x)=logsinximpliesf'(x)=cotx`
Hence function is increasing in the interval `(0,(pi)/2)`.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MISCELLANEOUS PROBLEMS|80 Videos
  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos
  • APPLICATIONS OF DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos
  • BINOMIAL DISTRIBUTION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

Similar Questions

Explore conceptually related problems

In the interval (0, (pi)/(2)) the function f (x) = cos ^(2) x is :

Consider the following statements : 1. The function f(x)=sinx decreases on the interval (0,pi//2) . 2. The function f(x)=cosx increases on the interval (0,pi//2) . Which of the above statements is/are correct ?

Consider the following statements I.The function f(x)=x^(2)+2cos x is increasing in the interval (0,pi). II.The function f(x)=ln(sqrt(1+x^(2))-x) is decreasing in the interval (-oo,oo). Which of the above statement(s) is/are correct?

Find the intervals in which the function 'f' given by : f(x)=sinx-cosx, 0lexle2pi is strictly increasing or striclty decreasing.

If log_(cosx)sin x ge 2 and 0le xle 3pi , then the value of sinx lies in the interval (0, (sqrta-b)/(2)] then value of a-b is

The length of the longest interval in which the function y=sin2x-2sinx increases for x in [0, pi] is

On which of the following intervals is the function f given by f(x)=x^(100)+sinx-1 strictly decreasing ? (A) (0, 1) (B) (pi/2,pi) (C) (0,pi/2) (D) None of these

The value of c in Lagranges theorem for the function f(x)=log sin x in the interval [(pi)/(6),(5 pi)/(6)] is (pi)/(4) (b) (pi)/(2)(2 pi)/(3) (d) none of these

In the interval [-pi/4,pi/4] the number of real solutions of the equations |[sinx , cosx ,cosx],[cosx, sinx, cosx],[cosx , cosx , sinx]| =0

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DERIVATIVES-MHT CET CORNER
  1. On the interval (0,(pi)/2) the function log sinx is

    Text Solution

    |

  2. If the Rolle's theorem for f(x)=e^(x)(sin x-cosx) is verified on [(pi)...

    Text Solution

    |

  3. The approximate value of f(x)=x^(3)+5x^(2)-7x+9 at x=1.1 is

    Text Solution

    |

  4. एक कण वक्र 6y= x^3+ 2 के अनुगत गति कर रहा है वक्र पर उन बिंदुओं को ज...

    Text Solution

    |

  5. All points on the curve y^(2)=4a(x+a" sin"(x)/(a)) at which the tangen...

    Text Solution

    |

  6. The length of normal at any point to the curve, y=c cosh(x/c) is

    Text Solution

    |

  7. The height of right circular cylinder of maximum volume in a sphere of...

    Text Solution

    |

  8. x,के सभी वास्तविक मानों के लिए (1-x+x^2)/(1+x+x^2) का न्यूनतम मान है ...

    Text Solution

    |

  9. If x+y=k is normal to y^2=12 x , then k is 3 (b) 9 (c) -9 (d) -3

    Text Solution

    |

  10. A particle moves along a straight line according to the law s=16-2t+3t...

    Text Solution

    |

  11. The equation of the tangent at (2,3) on the curve y^2=a x^3+b is y=4x-...

    Text Solution

    |

  12. The equation of motion of a particle moving along a straight line is s...

    Text Solution

    |

  13. The equation of the tangent to the curve y=4xe^(x) at (-1,(-4)/e) is

    Text Solution

    |

  14. The abscissa of the points, where the tangent to curve y=x^(3)-3x^(2)-...

    Text Solution

    |

  15. The point of the curve y^(2)=2(x-3) at which the normal is parallel to...

    Text Solution

    |

  16. Maximum area of a reactangle which can be inscribed in a circle of a...

    Text Solution

    |

  17. If the function f(x)=2x^3-9a x^2+12 x^2x+1,w h e r ea >0, attains its ...

    Text Solution

    |

  18. If f(x)= kx-sin x is monotonically increasing then

    Text Solution

    |

  19. If a particle moves such that the displacement is proportional to the ...

    Text Solution

    |

  20. f(x)=tan^(-1)(sinx+cosx), x gt0 is always and increasing function on t...

    Text Solution

    |

  21. A ladder 10 m long rests against a vertical wall with the lower end on...

    Text Solution

    |