Home
Class 12
MATHS
If f(x)=x-[x], where [x] is the greatest...

If f(x)=x-[x], where [x] is the greatest integer less than or equal to x, then `f(+1/2)` is:

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|4 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If f(x)=e^([cotx]) , where [y] represents the greatest integer less than or equal to y then

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] where [x] denotes the greatest integer less than or equal to x.

If f(x) = {{:((sin[x])/([x]),[x] != 0),(0,[x] = 0):} , where [x] denotes the greatest integer less than or equal to x, then lim_(x to 0) equals

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

If f(x)={("sin"[x])/([x]) ,for [x]!=0, 0 ,for[x]=0,where [x] denotes the greatest integer less than or equal to x , then lim_(x→0)f(x) is (a) 1 (b) 0 (c) -1 (d) none of these

Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):} and g: R to R be the greatest integer function given by g(x) = [x] where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

The period of sin""(pi[x])/12+cos""(pi[x])/4+tan""(pi[x])/3 , where [x] represents the greatest integer less than or equal to x is

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

f(x)= 1/sqrt([x]-x) , where [*] denotes the greatest integeral function less than or equals to x. Then, find the domain of f(x).

Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the greatest integer less than or equal to xdot Then, evaluate int_(-1)^1f(x)dx .

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

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

    Text Solution

    |

  3. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  4. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  5. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  6. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  7. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  8. Find x+y+z

    Text Solution

    |

  9. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  10. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  11. The value of int(In2)^(In3) (x sinx)dx is

    Text Solution

    |

  12. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

  13. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

    Text Solution

    |

  14. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

    Text Solution

    |

  15. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  16. Which of the following is true?

    Text Solution

    |

  17. f(x)={(x-[x]",",if[x] "is odd"),(1+[x]-x",",if[x]" is even"):} Then,...

    Text Solution

    |

  18. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  19. Let I(n)=int(-pi)^(pi)(sin x)/((1+pi^(x))sin x )dx, n=0,1,2,... The va...

    Text Solution

    |

  20. Let S(n)=sum(k=1)^(n)n/(n^(2)+kn+k^(2)) and T(n)=sum(k=0)^(n-1)n/(n^(2...

    Text Solution

    |