Home
Class 12
MATHS
The function f(x)=(sin(pi[x-pi]))/(4+[x]...

The function `f(x)=(sin(pi[x-pi]))/(4+[x]^2)` , where `[]` denotes the greatest integer function, (a) is continuous as well as differentiable for all `x in R` (b) continuous for all `x` but not differentiable at some `x` (c) differentiable for all `x` but not continuous at some `x` . (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    RD SHARMA ENGLISH|Exercise All Questions|441 Videos

  • DIFFERENTIAL EQUATION

    RD SHARMA ENGLISH|Exercise All Questions|646 Videos

Similar Questions

Explore conceptually related problems

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

Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

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

f(x)=[sinx] where [.] denotest the greatest integer function is continuous at:

The function f(x)={x} , where [x] denotes the greatest integer function , is continuous at

The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greatest integer function, is discontinuous

Let f(x) = (sin {pi[x-pi]})/(1+[x^(2)]) , where [.] stands for the greatest integer function. Then, f(x) is continuous or not?

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than ...

    Text Solution

    |

  2. Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f...

    Text Solution

    |

  3. The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the gre...

    Text Solution

    |

  4. Let f(x)={a x^2+1,x >1; x+1/2,x<=1.t h e n ,f(x) is derivable at x=1...

    Text Solution

    |

  5. Show that the function defined by g(x)= "x"-"[x] is discontinuous at a...

    Text Solution

    |

  6. It A is a symmetric matrix, write whether A^T is symmetric or skew - s...

    Text Solution

    |

  7. If f(x)={x^2+3x+a ,xlt=1, b x+2, forx >1 is everywhere differentiable...

    Text Solution

    |

  8. Let f(x)=|x| and g(x)=|x^3|, then (a)f(x)a n dg(x) both are continu...

    Text Solution

    |

  9. Is |sinx| differentiable? What about cos|x|?

    Text Solution

    |

  10. Find the values of aa n db so that the function f(x)={x^2+3x+a ,ifxlt=...

    Text Solution

    |

  11. The function f(x)=e^(-|x|) is continuous everywhere but not differenti...

    Text Solution

    |

  12. Discuss the continuity and differentiability of f(x)={1-x ,x<1 ...

    Text Solution

    |

  13. If y = (x-1)log(x-1)-(x+1)log(x+1), prove that : dy/dx = log((x-1)/(1+...

    Text Solution

    |

  14. The set of points where the function f(x)=x|x| is differentiable is ...

    Text Solution

    |

  15. The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). ...

    Text Solution

    |

  16. Let f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x) is continuous and dif...

    Text Solution

    |

  17. If f(x) = sqrt(1-(sqrt1-x^2)) , then f(x) is (a)continuous on [-1, ...

    Text Solution

    |

  18. If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 the...

    Text Solution

    |

  19. Solve the following equation for x : cos(tan^-1 x) = sin(cot^-1(3/4))

    Text Solution

    |

  20. Find the principal values the following : sin^-1{cos(sin^-1(sqrt(3)/2)...

    Text Solution

    |