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

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 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 .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the inverse of the matrix [[1,2],[3,4]]

    Text Solution

    |

  2. Find the number of critical points of f(x)=frac[abs(x-1)][x^2]

    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. Find the equation of the tangent to the curve x = y^2-1 at the point w...

    Text Solution

    |

  5. If y=sin^(-1)(x^3), then find that dy/dx

    Text Solution

    |

  6. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

    Text Solution

    |

  7. Evaluate int0^2abs(x^2+2x-3)dx

    Text Solution

    |

  8. Find the area of the region bounded by the curve y=sin^(3)x and the st...

    Text Solution

    |

  9. intdx/(1+tanx)

    Text Solution

    |

  10. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

    Text Solution

    |

  11. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  12. Let veca,vecb,vecc be three vectors such that veca+vecb+vecc=vec0 and ...

    Text Solution

    |

  13. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

    Text Solution

    |

  14. Find the co-ordinates of the foot of the perpendicular from the point ...

    Text Solution

    |

  15. Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...

    Text Solution

    |

  16. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

    Text Solution

    |

  17. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

    Text Solution

    |

  18. Show that the sum of the intercepts on the coordinate axes of any tang...

    Text Solution

    |

  19. Find frac[dy][dx] if y=([sinx+x^2]/[cot2x]).

    Text Solution

    |

  20. Integrate intfrac[(sin^2x+cos2x)][cos^2x)]dx

    Text Solution

    |