Home
Class 11
MATHS
If f(x)={(sin{cosx}/(x-pi/2), x ne pi/2)...

If `f(x)={(sin{cosx}/(x-pi/2), x ne pi/2),(1, x=pi/2):}` , where {.} denotes the fractional part of x, then f(x) is :

A

continuous at `x=pi/2`

B

`lim_(xrarrpi/2)f(x)`, but f(x) is not continuous at `x=pi/2`

C

`lim_(xrarrpi/2)` does not exists

D

`lim_(xrarr(pi^-)/2)f(x)=1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Period of f(x)=cos2pi{x} is , where {x} denote the fractional part of x)

If f'(x)=|x|-{x} where {x} denotes the fractional part of x, then f(x) is decreasing in (-1/2, k) , find k.

If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , then f(x) is decreasing in (a) (-1/2,0) (b) (-1/2,2) (-1/2,2) (d) (1/2,oo)

The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {x} denotes the fractional part of x) is

Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes the greatest integer less than or equal to x). The number of points, where f(x) is discontinuous is

The domain of the function f(x)=1/(sqrt({sinx}+{sin(pi+x)})) where {dot} denotes the fractional part, is (a) [0,pi] (b) (2n+1)pi/2, n in Z (c) (0,pi) (d) none of these

If f(x)= cos [ pi^(2)] x+ cos[ -pi^(2)] x where [x] denotes the greatest integer function, then show that f(-pi)=0

If f(x)={x^2 sin((pi x)/2), |x| =1 then f(x) is

If f(x)=sin([x]pi)/(x^2+x+1) where [.] denotes the greatest integer function, then (A) f is one-one (B) f is not one-one and not constant (C) f is a constant function (D) none of these

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) (cos^2(1-cos^2(1-cos^2.......cos^2(x)......)))/(sin[pi((sqrt(x+4) - 2)/x) ]

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f(x)=-1+|x-2|, 0lexle4 g(x)=2-|x|, -1lexle3 Then, fog(x) is contin...

    Text Solution

    |

  2. Let f(x)=[sinx + cosx], 0ltxlt2pi, (where [.] denotes the greatest int...

    Text Solution

    |

  3. If f(x)={(sin{cosx}/(x-pi/2), x ne pi/2),(1, x=pi/2):} , where {.} den...

    Text Solution

    |

  4. If f(x)=(x^3+x^2-16x+20)/(x-2)^2, x ne 2 =k, x=2 and if f(x) is con...

    Text Solution

    |

  5. In the function f(x)=[(x-2)^3/a]sin(x-2)+acos(x-2), (where [.] denote...

    Text Solution

    |

  6. Let f(x) = |x|+|sin x|, x in (-pi/2, (3pi)/2). Then, f is :

    Text Solution

    |

  7. If f is a periodic function, then

    Text Solution

    |

  8. If f(x)=[sin^2x] (where [.] denotes the greatest integer function ) th...

    Text Solution

    |

  9. Let f(x) be a polynomial of degree one and f(x) be a function defined ...

    Text Solution

    |

  10. lim(xrarr0)(e^cotx-e^cosx)/(cotx-cosx) is

    Text Solution

    |

  11. value of lim(xrarrinfty)((x+1)/(x+2))^(2x+1) is

    Text Solution

    |

  12. lim(xrarrinfty)(3^x+4^(x+1)+5^x)/(5^x+3^(x+1)) is

    Text Solution

    |

  13. lim(xrarrinfty)[((2+x)^40(4+x)^5)/(2-x)^45] equals

    Text Solution

    |

  14. lim(xrarr5)(x-5)/|x-5| equals to

    Text Solution

    |

  15. lim(x rarr pi/3)frac(Sin(pi/3-x))(2cosx-1) is equal to

    Text Solution

    |

  16. If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xrarrinfty)f(x)=

    Text Solution

    |

  17. If lim(xrarrinfty)((x^2+1)/(x+1)-px-q)=0, then

    Text Solution

    |

  18. The value of lim(xrarrinfty)frac(x^3sin(1/x)-2x^2)(1+3x^2)is

    Text Solution

    |

  19. If f(x)={(sin[x]/[[x]], "for"[x] ne 0),(0, "for"[x] = 0):} where [x] d...

    Text Solution

    |

  20. The number of points at which the function f(x)=1/log|x| is discontinu...

    Text Solution

    |