Home
Class 12
MATHS
g:[0,pi]toR is defined as g(x)={("max"{"...

`g:[0,pi]toR` is defined as `g(x)={("max"{"sin"x,1/2},"where",x epsilon[0,(pi)/2]),("min"{"sin"x,1/2},"where",x epsilon((pi)/2,pi]):}`
then answer following question
`lim_(to(pi^(-))/2)g(x)-lim_(xto(pi^(+))/2)g(x)` is equal to

A

`1`

B

`-1`

C

`1/2`

D

`-1/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

g:[0,pi]toR is defined as g(x)={("max"{"sin"x,1/2},"where",x epsilon[0,(pi)/2]),("min"{"sin"x,1/2},"where",x epsilon((pi)/2,pi]):} then answer following question g(x) is not differentiable in (0,pi)

lim_(xto0)(3-3tan((pi)/4-x))/(sin2x) is equal to

lim _(xto (pi)/(3 )) (sin ((pi)/(3)-x))/( 2 cos x-1) is equal to:

lim_(x to pi/2) (tan2x)/(x-(pi)/(2))

Lim_(x to pi/2) (1-sin x)/((pi/2-x)^(2))

Lim_( x to pi/2) (1-sin x)/((pi-2x)^(2))

Evaluate lim_(xto(pi)/(2)) (1+cos2x)/((pi-2x)^(2)).

Evaluate the following limits: Lim_( x to pi/2 )(1-sin x)/((pi/2-x)^(2))

Evaluate the following limit : Lim_(x to pi/2) (1+cos 2x)/(pi-2x)^(2)

Evaluate the following limits: lim_(xto pi)(sqrt(2+cosx)-1)/((pi-x)^(2))

ALLEN-TEST PAPERS-MATHEMATICS
  1. If int tan^(5) x dx = A tan^(4)x + B tan^(2) x+ g (x)+C, then

    Text Solution

    |

  2. g:[0,pi]toR is defined as g(x)={("max"{"sin"x,1/2},"where",x epsilon[0...

    Text Solution

    |

  3. g:[0,pi]toR is defined as g(x)={("max"{"sin"x,1/2},"where",x epsilon[0...

    Text Solution

    |

  4. Graph of y=f(x) is shown in the adjacent figure Value of lim(0^(...

    Text Solution

    |

  5. If f(x)=|x-1|+|x-3|,then value of f'(2) is equal to

    Text Solution

    |

  6. if y=(secx+tanx-1)/((-secx)+tanx+1), then find(dy)/(dx) at x=(pi)/(4).

    Text Solution

    |

  7. Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=...

    Text Solution

    |

  8. If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta...

    Text Solution

    |

  9. The number of solution of the equation 2(tanx-sinx)+3(cotx-cosx)+5=0x ...

    Text Solution

    |

  10. If n^(th) term (T(n)) of the sequece is given by the relation T(n+1)=T...

    Text Solution

    |

  11. If lamda(1) is the product of values of x satisfy the equation (x)^(lo...

    Text Solution

    |

  12. If (2tan^(2)theta(1)tan^(2)theta(2)tan^(2)theta(3)+tan^(2)theta(1)tan^...

    Text Solution

    |

  13. Value of "sin"^(6)(pi)/16+"sin"^(6)(3pi)/16+"sin"^(5pi)/16+"sin"^(6)(7...

    Text Solution

    |

  14. Number of solution of the equation sin^(2)x+(sin^(2)3x)/4=sinx sin 3x,...

    Text Solution

    |

  15. If x and y are real and satisfy the equation x^(2)+16y^(2)-3x+2=0 then...

    Text Solution

    |

  16. If a,b,c,d,e are positive numbers, then which of the following holds g...

    Text Solution

    |

  17. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

  18. Statement I cos^(3)alpha+cos^(3)(alpha+(2pi)/(3))+cos^(3)(alpha+(4pi)/...

    Text Solution

    |

  19. Find the values of a and b if f is continuous at x=0, where f(x)={:...

    Text Solution

    |

  20. Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the...

    Text Solution

    |