Home
Class 11
MATHS
if f(x)=[sqrt2sinx], where [x] denotes t...

if `f(x)=[sqrt2sinx]`, where [x] denotes the greatest integer function, then

A

f(x) is continuous at x=0

B

maximum value of f(x) is 1 in interval `[-2pi,2pi]`

C

f(x) is discontinuous at `X=(npi)/2+pi/4`, `ninI`

D

f(x) is differentiable at `x=npi, ninI`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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

If f : R to [-1, 1] , where f(x)=sin(pi/2[x]) (where [.] denotes the greatest integer function), then the range of f(x) is

If f(x)=sin sqrt([a])x , (where [.] denotes the greatest integer function), has pi as it's fundamental period, then

Let f : (4, 6)to(6, 8) be a function defined by f(x) x+[x/2] (where [.] denotes the greatest integer function), then f^(-1)(x) is equal to

If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer function), then f (x) is

Given lim_(x to 0)(f(x))/(x^(2))=2 , where [.] denotes the greatest integer function, then which options are correct?

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

Find the inverse of the function: f:Z to Z defined by f(x)=[x+1], where [.] denotes the greatest integer function.

Let f(x) = [x^3 - 3] where [.] denotes the greatest integer function Then the number of points in the interval ( 1, 2) where the function is discontinuous, is

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x)=[tan^2x], where [.]denotes the greatest integer function. The...

    Text Solution

    |

  2. If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) ...

    Text Solution

    |

  3. if f(x)=[sqrt2sinx], where [x] denotes the greatest integer function, ...

    Text Solution

    |

  4. f(x)=[x]+|x-1| then f(x), where [.] denotes greatest integer function)...

    Text Solution

    |

  5. If f(x)={(-x, x le 1),(3+x, x gt1):}, g(x)= {(x^2, x le 1),(2-x,x gt 1...

    Text Solution

    |

  6. If {x} denotes the fractional part of x, then lim(xrarr0)(e^{x}-1)/x i...

    Text Solution

    |

  7. Consider f(x)={(x^2/|x|, x ne 0),(0, x=0):}

    Text Solution

    |

  8. Value of lim(x rarr 3)(sin(e^(x-3) -1))/log(x-2) is

    Text Solution

    |

  9. lim(x rarr 1) x^(1//1-x) is

    Text Solution

    |

  10. lim(x rarr 0) ((1+tan x)/(1-tan x))^(1/x) is

    Text Solution

    |

  11. The value of lim(x rarr 0) (int0^(x^2)sec^2tdt)/(x sinx) is :

    Text Solution

    |

  12. The value of lim(x rarr 0) |cosx + sinx|/x^2 is equal to

    Text Solution

    |

  13. lim(x rarr infty)(root(2)(x^2 + 1)-root(3)(x^2 + 1))/(root(4)(x^2 + 1)...

    Text Solution

    |

  14. The value of a, b and c such that lim(x rarr 0) (ae^x -b cosx + ce^(...

    Text Solution

    |

  15. Let f(x) = lim(n rarr infty)(sinx)^(2n), then f is

    Text Solution

    |

  16. The set of all points where the function f(x)= x/(1+|x|) is differenti...

    Text Solution

    |

  17. Let f(x) = (x(1+a cosx) - b sinx)/x^2, x ne 0 and f(0) = 1

    Text Solution

    |

  18. If x + |y| = 2y, then y as a function of x is :

    Text Solution

    |

  19. Let [x] denotes the greatest integer less than or equal to x, If (x) =...

    Text Solution

    |

  20. The function f(x) = {(|x-3|, x ge 1), (x^2/4-(3x)/2+13/4, x lt1):}

    Text Solution

    |