Home
Class 12
MATHS
Consider f(x)=[[2(sinx-sin^3x)+|sinx-si...

Consider `f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx-sin^3x|]], x != pi/2` for `x in (0,pi), f(pi/2) = 3` where [ ] denotes the greatest integer function then,

A

f is continuous and differentiable at `x = pi//2`

B

f is continuous but not differentiable at `x = pi//2`

C

f is neither continuous nor differentiable at `x = pi//2`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x) =[ sin ^(-1)(sin 2x )] (where, [] denotes the greatest integer function ), then

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

f(x)=sin^(-1)((2-3[x])/4) , which [*] denotes the greatest integer function.

f(x)=sin^(-1)[2x^(2)-3] , where [*] denotes the greatest integer function. Find the domain of f(x).

If [sin x]+[sqrt(2) cos x]=-3 , x in [0,2pi] , (where ,[.] denotes the greatest integer function ), then

The period of the function f(x)=Sin(x +3-[x+3]) where [] denotes the greatest integer function

int (sin2x-sinx)/(sin^2x+cosx+3) dx

Discuss the continuity and differentiability for f(x) = [sin x] when x in [0, 2pi] , where [*] denotes the greatest integer function x.

Number of points of non-differerentiable of f(x)=sin pi(x-[x])"in "(-pi//2,[pi//2). Where [.] denotes the greatest integer function is

Find whether the given function is even or odd: f(x)=(x(sinx+tanx)/([x+pi/pi]-1/2); whether [] denotes the greatest integer function.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  2. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  3. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  4. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  5. The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not dif...

    Text Solution

    |

  6. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  7. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f...

    Text Solution

    |

  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made...

    Text Solution

    |

  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  10. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |

  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  12. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

    Text Solution

    |

  13. If x dy = y (dx + y dy), y > 0 and y (1) = 1, then y (−3) is equal t...

    Text Solution

    |

  14. Let f(x) be continuous and differentiable function for all reals and f...

    Text Solution

    |

  15. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  17. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

    Text Solution

    |

  18. Number of points of non-differentiability of the function g(x) = [x^2...

    Text Solution

    |

  19. Find dy/dx if y= xtanx

    Text Solution

    |

  20. If f((x)/(y))=(f(x))/(f(y)) forall x, y in R, y ne 0 and f'(x) exists ...

    Text Solution

    |