Home
Class 12
MATHS
If the function and the derivative of th...

If the function and the derivative of the function `f(x)` is everywhere continuous and is given by
`f(x)={:{(bx^(2)+ax+4", for " x ge -1),(ax^(2)+b", for " x lt -1):}`, then

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    BANSAL|Exercise All Questions|376 Videos
  • INTEGRALS

    BANSAL|Exercise All Questions|111 Videos

Similar Questions

Explore conceptually related problems

If f(x) continuous on its domain, where f(x)={:{(6", for " x le 2), (ax+b", for " 2 lt x lt 10),(22", for " x ge 10):} , then

If f(x) is continuous at x=2 and x=10 , where f(x)={:{(5", if " x le 2),(ax+b", if " 2 lt x lt 10),(21", if " x ge 10):} , then

The function f(x)= {(2 ax ", " x ge 3 ),( 3x +1 ", " x gt 3):} continuous at x= 3, then a =?

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

If f(x)=ax^(2)+bx+c, f(-1) gt (1)/(2), f(1) lt -1 and f(-3)lt -(1)/(2) , then

Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x) is derivable at x =1 , if

If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+ax+4,xge-1):} is every where continuous, then what are the values of a and b?

If the function f(x)={{:(k +x, "for " x lt1),(4x+3, "for " x ge1):} is continuous at x=1 then k=

BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f(x)=lim(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)). then

    Text Solution

    |

  2. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)),x!=1,2 6,x=...

    Text Solution

    |

  3. If the function and the derivative of the function f(x) is everywhere ...

    Text Solution

    |

  4. If the function f(x)=(3x^2+a x+a+3)/(x^2+x-2) continuous at x=-2.find...

    Text Solution

    |

  5. Find all possible values of a and b so that f(x) is continuous for all...

    Text Solution

    |

  6. The function f(x) = [{:((6/5)^(tan 6x)/(tan 5x), if, 0 lt x lt pi/2),(...

    Text Solution

    |

  7. Suppose that f(x)=x^3-3x^2 and h(x) =[(f(x))/(x-3), x!=3 then K , ...

    Text Solution

    |

  8. Let yn(x)=x^2+(x^2)/(1+x^2)+(x^2)/(1+x^2)^2+...(x^2)/(1+x^2)^(n-1) and...

    Text Solution

    |

  9. Find the number ofpoints of discontinuity of the function f(x)-[5x]+ {...

    Text Solution

    |

  10. Let f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)...

    Text Solution

    |

  11. Let [x] denote the greatest integer function & f(x) be defined in a ne...

    Text Solution

    |

  12. let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(l...

    Text Solution

    |

  13. Determine a & b so that f is continuous at x = pi/2 whre f(x) = [{:(...

    Text Solution

    |

  14. Discuss the continuity of 'f' in [0, 2], where f(x) = {{:(|4x - 5|[x],...

    Text Solution

    |

  15. If f(x0=x+{-x}+[x],\ w h e r e\ [x] is the integral part& {x} is th...

    Text Solution

    |

  16. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

    Text Solution

    |

  17. Let f(x)=lim(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is con...

    Text Solution

    |

  18. f(x)=(sinx+cosx)^(c o s e c x) ,-pi/2ltxlt0 a,x=0 (e^(1/x)+e^(2/x)+e...

    Text Solution

    |

  19. Let sum(r=1)^nsin^(- 1)alphar=(npi)/2 for any n in N and p=prod(r=1)...

    Text Solution

    |

  20. If the function f(x) =(tan(tanx)-sin(sinx))/(tanx-sinx) (x !=0): is c...

    Text Solution

    |