Home
Class 12
MATHS
If f(x)={{:("x sin"(1)/(x)",",xne0),(k",...

If `f(x)={{:("x sin"(1)/(x)",",xne0),(k",",x=0):}` is continuous at x=0, then the value of k is

A

1

B

`-1`

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
In Function f(x) is continuou at x=0, then
`f(0)= lim_(x to 0) f(x)`
Given, `f(0)=k`
`:. f(0)=k= lim_(x to 0) x "sin"(1)/(x)`
`rArr k=0 ( :. -1 le "sin"^(1)/(x) le 1)`
Promotional Banner

Topper's Solved these Questions

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

  • MHTCET 2009

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

If f(x)={((1-cos x)/(x)",",x ne 0),(k",",x=0):} is continuous at x = 0, then the value of k is

Select the write the most appropriate answer from the given alternatives in each of the following : {:(f(x)(sin5x)/(3x)",",xne0),(=k",",x=0.):} If f is continuous at x=0, then the value of k is

If f(x)={(x^(k) sin((1)/(x))",",x ne 0),(0",", x =0):} is continuous at x = 0, then

If f(x)={((3 sin pi x)/(5x)"," , xne 0),(2k",", x =0):} is continuous at x = 0, then the value of k is equal to

If the function f(X)={{:(,(cos x)^(1//x),x ne 0),(,k,x=0):} is continuous at x=0, then the value of k, is

The function f(x)={{:(sinx/x+cosx", if "xne0),(k", if "x=0):} is continuous at x = 0, then the value of 'k' is :

If f(x) = {((sin3x)/(x), x !=0),(k/2,x=0):} is continuous at x = 0, then the value of k is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MHTCET 2008-MATHEMATICS
  1. The chances to fail in Physis are 20% and the chances to fail in Mathe...

    Text Solution

    |

  2. lim(x to0)(cosax-cosbx)/(x^(2)) is equal to

    Text Solution

    |

  3. If f(x)={{:("x sin"(1)/(x)",",xne0),(k",",x=0):} is continuous at x=0,...

    Text Solution

    |

  4. The solution of the differential equation (dy)/(dx)=(x-y+3)/(2x(x-y)+5...

    Text Solution

    |

  5. If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)), then (dy)/(dx) is equal...

    Text Solution

    |

  6. The velocity of particle at time t is given by the relation v=6t-(t^(2...

    Text Solution

    |

  7. The maximum value of function f(x)=x^3-12 x^2+36 x+17 in the interval ...

    Text Solution

    |

  8. vec(a)xx[vec(a)xx(vecaxxvecb)] is equal to

    Text Solution

    |

  9. If one end of the diameter is (1, 1) and the other end lies on the lin...

    Text Solution

    |

  10. For the circuits shown below, the Boolean polynimial is

    Text Solution

    |

  11. Dual of (x'vvy')'=x^^y is

    Text Solution

    |

  12. Negation of the conditional ''If it rains, I shall go to school'' is

    Text Solution

    |

  13. The value of intxsinxsec^(3)xdx is

    Text Solution

    |

  14. The value of int underset(0)overset(pi) xsin^(3)xdx is

    Text Solution

    |

  15. A parents has two children. If one of them is boy, then the probabilit...

    Text Solution

    |

  16. For the LPP Min z=x(1)+x(2) such that inequalities 5x(1)+10x(2)ge0,x...

    Text Solution

    |

  17. Find ten equation of the plane passing through the point (0,7,-7) and ...

    Text Solution

    |

  18. Angle of intersection of the curve r=sintheta+costhetaand r=2sintheta ...

    Text Solution

    |

  19. The equation of the tangent parallel to y-x+5=0" drawan to "(x^(2))/(3...

    Text Solution

    |

  20. The volume of solid generated by revolving about the y-axis the figur...

    Text Solution

    |