Home
Class 12
MATHS
If the function f(x) defined by f(x)={...

If the function f(x) defined by
`f(x)={(x"sin"(1)/(x)",", "for "x ne 0),(k",", "for " x=0):}`
is continuous at x = 0, then k is equal to

A

0

B

1

C

-1

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    NIKITA PUBLICATION|Exercise MCQS|77 Videos
  • DEFINITE INTEGRAL

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|243 Videos

Similar Questions

Explore conceptually related problems

If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0, then k =

If f(x)={(log_((1-3x))(1+3x)",","for",x ne 0),(k",","for",x =0):} is continuous at x = 0, then k is equal to

If the function f(x) defined by f(x)={:{(xsin((1)/(x)),"for"xne0),(k,"for"x=0):} is continous at x=0 , then k=

Let f(x)={((sin pix)/(5x)",",x ne0),(k"," , x =0):} if f(x) is continuous at x = 0, then k is equal to

For what value of k, the function defined by f(x)={((log(1+2x)sin x^(@))/(x^(2))",", "for "x ne 0),(k",","for "x =0):} is continuous at x = 0 ?

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

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

If f(x) = {{:(sin1/x, x ne 0),(k, x =0):} , is continous at x=0, then k is equal to-

If the function f(x)={((1-cosx)/(x^(2))",","for "x ne 0),(k,"for " x =0):} continuous at x = 0, then the value of k is

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x) is continuous at x=0, where f(x)=(3-4cos x+cos 2x)/(x^(4)), f...

    Text Solution

    |

  2. The value of k which makes f(x)={:{(sin(1/x)", for " x!=0),(k", for "...

    Text Solution

    |

  3. If the function f(x) defined by f(x)={(x"sin"(1)/(x)",", "for "x ne ...

    Text Solution

    |

  4. If f(x) is continuous at x=a, where f(x)=(x-a)sin((1)/(x-a)), for x!=...

    Text Solution

    |

  5. If (x)=(1-sqrt3tanx)/(pi-6x),"for"x nepi/6 is continous at x=pi/6, "fi...

    Text Solution

    |

  6. Value of f(pi/4) so that the function f(x) = (tan(pi/4-x))/(cot 2x), ...

    Text Solution

    |

  7. Find the value of k, if the functions are continuous at the points giv...

    Text Solution

    |

  8. If f(x) is continuous at x=pi/2, where f(x)=(1-sin x)/((pi/2 -x)^(2))...

    Text Solution

    |

  9. If f(x) is continuous at x=pi/2, where f(x)=(1-sin x)/((pi-2x)^(2)), ...

    Text Solution

    |

  10. If f(x) is continuous at x=pi/2, where f(x)={:{((1-sinx)/(pi-2x)", fo...

    Text Solution

    |

  11. For what value of k, function f(x)={((k cosx)/(pi-2x)",","if "x ne (pi...

    Text Solution

    |

  12. If f(x) is contiuous at x= pi/2, where f(x)=(sec x - tan x)/(pi/2 - x...

    Text Solution

    |

  13. If f(x) is continuous at x = pi, where f(x)=(sqrt(2+cos x)-1)/((pi-x)...

    Text Solution

    |

  14. If f(x) is continuous at x=pi, where f(x)=(1- cos ( 7(x-pi)))/(5(x - ...

    Text Solution

    |

  15. If f(x) is continuous at x=0, where f(x)=(1+2x)^(1/x)", for " x!=0, ...

    Text Solution

    |

  16. If f(x) is continuous at x=0, where f(x)={:{((1+3x)^(1/x)", for " x !...

    Text Solution

    |

  17. If f(x) is continuous at x=0, where f(x)=((4-3x)/(4))^(8/x)", for " x...

    Text Solution

    |

  18. If f(x)= {:{((x^(2)-4)/(x-2)", for " x!=2),(5", for " x=2):}, then at ...

    Text Solution

    |

  19. If f(x)={:{(root(3)((4x+1)/(1-4x))", for " x!=0),(e^(6)", for " x=0):}...

    Text Solution

    |

  20. If f(x) is continuous at x=0, where f(x)=((4-3)/(4+5x))^(1/x)", for "...

    Text Solution

    |