Home
Class 11
MATHS
The function f(x)=tan{pi[x-pi/2]}/(2+[x^...

The function `f(x)=tan{pi[x-pi/2]}/(2+[x^2]` , where [x] denotes the greatest integer `le x,` is

A

continuous for all values of `x`

B

discontinuous at `x=pi/2`

C

not differentiable for some values of `x`

D

discontinuous at x=-2

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

The function f(x)=(tan{pi[x-(pi)/(2)]})/(2+[x]^(2)) where [x] denotes the greatest integer ltx , is-

The function f(x) = [x]^2-[x^2] (where [.] denotes the greatest integer function ) is discontinuous at

If [x+[2x]] lt3 , where [.] denotes the greatest integer function, then x is

The period of the function f(x)= [6x+7]+cospix-6x , where [dot] denotes the greatest integer function is:

If T is the period of the function f(x)=[8x+7]+|tan2pix+cot2pix|-8x] (where [.] denotes the greatest integer function), then the value of 1/T is ___________

If T is the period of the function f(x)=[8x+7]+|tan2pix+cot2pix|-8x (where [.] denotes the greatest integer function), then the value of 1/T is ___________

In the function f(x)=[(x-2)^3/a]sin(x-2)+acos(x-2), (where [.] denotes the greatest integer function ) is continuous and differentiable in (4,6), then

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number

If f: R rarr R is a function defined by f(x)=[x]cos((2x-1)/2)pi , where [x] denotes the greatest integer function, then f is

If [2sinx]+[cosx]=-3 then the range of the function f(x)=sinx+sqrt3cosx in [0, 2pi] is, (where [.] denotes the greatest integer function)

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(xrarr0)sin(picos^2x)/x^2 is equal to :

    Text Solution

    |

  2. If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i ...

    Text Solution

    |

  3. The function f(x)=tan{pi[x-pi/2]}/(2+[x^2] , where [x] denotes the gre...

    Text Solution

    |

  4. Let f(x) be a differentiable function and f'(4)=5. Then lim(xrarr2)(f...

    Text Solution

    |

  5. The value of lim(xrarr0)(int0^(x^2) cos(t^2)dt)/(xsinx) is

    Text Solution

    |

  6. If lim(xrarr0)(2asinx-sin2x)/tan^3x exists and is equal to 1, then the...

    Text Solution

    |

  7. The function f(x)=a sin |x| +be^|x| is differentiable at x=0 when

    Text Solution

    |

  8. let f(x)={( int0^x|1-t|dt, xgt1),(x-1/2, xle1):} then

    Text Solution

    |

  9. The number of points in (-infty,infty) , for which x^3-xsin x-cos x =0...

    Text Solution

    |

  10. lim(xrarr0)((1-cos2)(3+cos x))/(xtan 4x) is equal to

    Text Solution

    |

  11. The limit of xsin (e^(1//x)) as xrarr0

    Text Solution

    |

  12. Let f(x)={f(x={(x^3-3x+2, xlt2),(x^3-6x^2+9x+2, xge2):} Then

    Text Solution

    |

  13. The limit of sum(n=1)^1000(-1)^n x^n as xrarrinfty

    Text Solution

    |

  14. The limit of [1/x^2+(2013)^x/(e^x-1)-1/(e^x-1)] as xrarr0

    Text Solution

    |

  15. The limit of {1/xsqrt(1+x)-sqrt(1+1/x^2} as xrarr0

    Text Solution

    |

  16. If lim(xrarrinfty)((x^2+x+1)/(x+1)-ax-b)=4 ,then

    Text Solution

    |

  17. Let f(x)={(x^2|cos"pi/x|, x ne0),(0, x=0):}, x in R, then f is

    Text Solution

    |

  18. Let alpha(a) and beta(b) be the roots of the equation , (root(3)(1+a)...

    Text Solution

    |

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

    Text Solution

    |

  20. If f: R rarr R is a function defined by f(x)=[x]cos((2x-1)/2)pi, where...

    Text Solution

    |