Home
Class 12
MATHS
Let : f(x)={((a+3cosx)/(x^2) ,, x<0),(bt...

Let : `f(x)={((a+3cosx)/(x^2) ,, x<0),(btan(pi/([x+3])) ,, xgeq0):}` If `f(x)` is continuous at `x=0,` then find `a \ a n d \ b` , where `[dot]` denotes the greatest integer function.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = {((x^2-4)/(x+2), x lt -3), (Ina, x=-3), (a+bx, x gt -3):} . For what value of a and b is f(x) continuous on the real line?

Let f(x)={((a(1-sinx)+b.cosx+5)/x^2,xlt0),(3, x=0),((1+((cx+dx^3)/x^2))^(1//x),xgt0):} find a and b

Let f(x) = 3/( 3x^2 + 9) and g(x)= x^2/( 3x^2 + 9) int (f(x) + g(x)) dx = ?

Let f(x) = 3/( 3x^2 - 9) and g(x)= x^2/( 3x^2 - 9) int (g(x) - f(x)) dx is equal to ?

Let f(x)=sin x+cosx and g(x)=x^(2)-1 , then g{f(x)} is invertible if -

" Let f(x) " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f' (pi//2) .

Let f(x)= |{:(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0):}| ,"then find " 1/piint_0^(pi/2)[f(x)+f'(x)]dx.

Let f(x)={(sinx+cosx",",0 lt x lt (pi)/(2)),(a",",x=pi//2),(tan^(2)x+"cosec"x",",pi//2 lt x lt pi):} Then its odd extension is

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 ...

    Text Solution

    |

  2. If the function f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, ...

    Text Solution

    |

  3. Let : f(x)={((a+3cosx)/(x^2) ,, x<0),(btan(pi/([x+3])) ,, xgeq0):} If...

    Text Solution

    |

  4. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of...

    Text Solution

    |

  5. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

    Text Solution

    |

  6. f(x)={cos^(-1){cotx), x<pi/2 pi[x]-1, x >pi/2 where [dot] represe...

    Text Solution

    |

  7. Discuss the differentiability of f(x)=|(log)ex| ,x>0

    Text Solution

    |

  8. Discuss the differentiability of f(x)="max"{sec^(-1)x , cosec^(-1)x}

    Text Solution

    |

  9. A function f(x) is such that f(x+pi/2)=pi/2-|x|AAx. Find f(pi/2), if i...

    Text Solution

    |

  10. Discuss the differentiability of f(x)=|x-1|+|x+1|

    Text Solution

    |

  11. Which of the function is non-differential at x=0? f(x)=|"x"^3|

    Text Solution

    |

  12. Discuss the differentiability of f(x)=|x^3| at x=0

    Text Solution

    |

  13. Discuss the differentiability of f(x)=|x|sinx+|x-2|sgn(x-2)+|x-3|dot

    Text Solution

    |

  14. Discuss the differentiability of f(x)="sin"|x|

    Text Solution

    |

  15. Discuss the differentiability of f(x)=[x]+|1-x|, x in (-1,3),w h e r e...

    Text Solution

    |

  16. Discuss the differentiability of f(x)=(x^2-1)|x^2-x-2|+sin(|x|)dot

    Text Solution

    |

  17. Let f be a function satisfying f(x+y)+sqrt(6-f(y))=f(x)f(y)a n df(h)->...

    Text Solution

    |

  18. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

    Text Solution

    |

  19. A function f(x) satisfies the following property: f(x+y)=f(x)f(y)dot S...

    Text Solution

    |

  20. Find the points of discontinuity of the function: f(x)=1/(2sinx-1)

    Text Solution

    |