Home
Class 12
MATHS
If f(x)={(ax^2+b if x lt1),(1 if x=1),(2...

If `f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):}`
is continuous at x=1, then find a and b.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 3

    MODERN PUBLICATION|Exercise PROBLEM|63 Videos

  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 Videos

Similar Questions

Explore conceptually related problems

If the function f(x)={:{(3ax+b", if "xgt1),(11", if "x=1),(5ax-2b", if "xlt1):} is continuous at x=1 , then find the values of a and b

If the function f(x) defined by f(x)={((log(1+ax)-log(1-bx))/(k)", if "x!=0),(" k, if "x=0):} is continuous at x=0 , then find the value of k.

Is the function f defined by f(x)={(x", if "xle1),(5", if "xgt1):} continuous at x=0, at x=1 and at x=2 ?

Find the relationship between a and b so that the function f defined by f(x)={(ax+1" , if "xle3),(bx+3" , if "xgt3):} is contunuous at x=3.

For what value of lamda is the function f(x)={{:(lamda(x^(2)-2x)", if "xle0),(4x+1", if "xgt0):} continuous at x=0 ? What about continuity at x=1 ?

Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", if "-1lexlt0),(" "(2x+1)/(x-1)", if "0lexlt1):} is continuous at x = 0

Find the relationship between a and b so that thefunction defined by f(x)={(ax+b,if,xle3),(bx+3, if, x>3):} s continuous at x = 3.

Find the values of a and b such that the function f defined by f(x)={:{((x-4)/(|x-4|)+a", if "xlt4),(a+b", if "x=4" is a"),((x-4)/(|x-4|)+b", if "xgt4):} continuous function at x=4 .

Show that f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 lt x lt 2):} is continuous at x = 1 .

MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

    Text Solution

    |

  2. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

    Text Solution

    |

  3. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

    Text Solution

    |

  4. Show that 2 sin x + than x ge 3x all x in (0, pi/20).

    Text Solution

    |

  5. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

    Text Solution

    |

  6. Evaluate the following integrals int(dx)/(sinx(3+2cosx) put cosx=z

    Text Solution

    |

  7. int0^(pi//2)(sqrttanx+sqrtcotx)dx

    Text Solution

    |

  8. Determine the area of the region bounded by y^2=x^3 and the double ord...

    Text Solution

    |

  9. Vectors vec(a), vec(b) and vec(c) are such that vec(a) + vec(b) + vec(...

    Text Solution

    |

  10. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

    Text Solution

    |

  11. Find the equation of the plane Which contains the line of intersection...

    Text Solution

    |

  12. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  13. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  14. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

    Text Solution

    |

  15. Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from...

    Text Solution

    |

  16. A variable plane meets the coordinate axes at A, B, C and is at a cons...

    Text Solution

    |

  17. Find x and y if [[1,3],[2,-1]][[x],[y]] = [[4],[1]].

    Text Solution

    |

  18. If [[3,5,3],[2,4,2],[lambda,7,8]] is a singular matrix, write the valu...

    Text Solution

    |

  19. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

    Text Solution

    |

  20. Express the value of "cosec"("cos"^(-1) 3/5 +"cos"^(-1) 4/5) in simple...

    Text Solution

    |