Home
Class 12
MATHS
Determine f(0) so that the function f(x)...

Determine f(0) so that the function f(x) defined by `f(x)=((4^(x)-1)^(3))/("sin "(x)/(4)"log"(1+(x^(2))/(3)))` becomes continuous at `x=0`.

Text Solution

Verified by Experts

The correct Answer is:
`12(log_(e)4)^(3)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise (PART II) Sample Question |11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise (PART II) QUESTION FOR PRACTICE (1 MARK) |26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise (PART I) QUESTION FOR PRACTICE (1 MARK) |8 Videos

  • CHSE ODISHA EXAMINATION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|11 Videos

  • DETERMINANTS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE |39 Videos

Similar Questions

Explore conceptually related problems

Write the domain of the function defined by f(x)= sin^(-1)x+cosx

Find the value of a, so that the function f(x) is defined by f(x)={{:((sin^(2)"ax")/(x^(2))", "x!=0),("1, "x=0):} may be continuous at x=0.

Find the value of a such that the function f defined by f(x)={{:((sinax)/(sinx), "if", x ne 0),((1)/(a), "if", x=0):} is continuous at x=0

Find the value of a such that the function f defined by f(x)={((sinax)/(sinx) if xne0),(1/a if x=0):} is continuous at x=0.

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Find the value of k so that the function f defined by f(x)={((kcos x)/(pi-2x)),when x!=pi/2),(0,atx=pi/2):} is continuous at x = (pi)/2 .

Examine the continuity of the function f defined by f(x) = {[2x+1if x 1]:} .

Show that the function f defined by f(x)={(x if "x is rational"),(-x if "x is irrational"):} is continuous at x=0 AAxne0inR

Determine whether the function f:X rarr Y defined by f(x) = 4x + 7, x in X is one-one.

Find the value of k, so that the function defined by f(x)={(kx+1", if "xlepi),(cosx", if "xgtpi):} is continuous at x=pi .

ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -(PART I) QUESTION FOR PRACTICE (4 MARK)
  1. If f(x)=(sqrt(2)cosx-1)/(cotx-1),x!=(pi)/(4). Then, find value of f((p...

    Text Solution

    |

  2. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

    Text Solution

    |

  3. Determine f(0) so that the function f(x) defined by f(x)=((4^(x)-1)^(3...

    Text Solution

    |

  4. Examine the continuity of a function f(x)={{:(|x|"cos"(1)/(x)", if ...

    Text Solution

    |

  5. Show that the function f(x)={{:((e^(1//x)-1)/(e^(1//x)+1)", when "x!=0...

    Text Solution

    |

  6. For what value of lamda is the function f(x)={{:(lamda(x^(2)-2x)", i...

    Text Solution

    |

  7. Find the value of k, so that the function defined by f(x)={(kx+1", if...

    Text Solution

    |

  8. For what value of k, the function f(x)={((tan2x)/(x)", if "x!=0),(k"...

    Text Solution

    |

  9. For what value of k the following function is continuous at x=0 ? f(...

    Text Solution

    |

  10. Find the value of a, so that the function f(x) is defined by f(x)={{...

    Text Solution

    |

  11. Show that the function f(x)={(|x-a|sin(1)/(x-a)", if "x!=a),(0", ...

    Text Solution

    |

  12. A car driver is driving a car on the dangerous path given by f(x)={((1...

    Text Solution

    |

  13. For what value of k, the function f(x)={{:((sin2x)/(x)", "x!=0),(k"...

    Text Solution

    |

  14. Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", ...

    Text Solution

    |

  15. find the value of k, so that the function f(x)={((2^(x+2)-16)/(4^(x)...

    Text Solution

    |

  16. Find the values of a and b such that the function f defined by f(x)={:...

    Text Solution

    |

  17. Discuss the continmuity of function f defined by f(x)={{:((1)/(2)-x"...

    Text Solution

    |

  18. Discuss the continuity of the function f(x)=sin x-cos x.

    Text Solution

    |

  19. Given, f(x)=(1)/(x-1). Find the points of discontinuity of composite f...

    Text Solution

    |

  20. Examine that sin|x| is a continuous function.

    Text Solution

    |