Home
Class 12
MATHS
The value of k which makes f(x)={{:(si...

The value of k which makes
`f(x)={{:(sinx,xne0),(k,x=0):}"continuous at x=0,is"

A

2

B

1

C

`-1`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)={{:(sinx",",xne0),(k",",x=0):}`
Given, f(x) is continuous at x=0
`underset(xto0)limf(x)=f(0)`
`impliesunderset(xto0)limsinx=k`
`impliesk=0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

The value of k which makes f(x)={(sin x)/(x),x!=0, and k,x=0 continuous at x=0, is (a) 8 (b) 1(c)-1 (d) none of these

f(x)={{:(sinx/x", " xne0),(k-1", " x=0):} is continuous at x = 0, then 'k' is :

The value of k which makes f(x)={:{(sin(1/x)", for " x!=0),(k", for " x=0):} continuous at x=0 is

If the function f(x)={{:(sinx,xne0),(k,x=0):} is continuous at x = 0 than find the value of k?

The value of k which makes f(x) = {((sin(1/x)), ",", x != 0),(k, ",",x = 2):} continuous at x = 0 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 the function f(x) defined by f(x)={:{(xsin((1)/(x)),"for"xne0),(k,"for"x=0):} is continous at x=0 , then k=

For what value of k is the function f(x)={k(|x|)/(x),x =0 continuous at x=0?

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. What is lim(x to 0) (tanx)/(sin2x) equal to?

    Text Solution

    |

  2. What is lim(h to 0) (sqrt(2x+3h)-sqrt2x)/(2h) equal to?

    Text Solution

    |

  3. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  4. Let A=(X"inR:-1lexle1)andS be the subset of AxxB, defined by S=[(x,y)i...

    Text Solution

    |

  5. If f(x)=sqrt(x-1)/(x-4) defines a function of R, then what is its doma...

    Text Solution

    |

  6. Consider the function f(x)={{:((sin2x)/(5x),if ,xne0),((2)/(15),if,x...

    Text Solution

    |

  7. For the function f(x)=|x-3|, which of the following is not correct?

    Text Solution

    |

  8. If the function f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at ea...

    Text Solution

    |

  9. If f(x )=sqrt(25-x^(2)), then what is lim(x to 1) (f(x)-f(1))/(x-1) eq...

    Text Solution

    |

  10. What is lim(thetato0)(sqrt(1-costheta))/(theta) equal to?

    Text Solution

    |

  11. A function f:AtoR is defined by the equation f(x)=x^(2)-4x+5 where A...

    Text Solution

    |

  12. In which one of the following intervals is the function f(x)=x^(2)-5x...

    Text Solution

    |

  13. Let f(x+y)=f(x)f(y)andf(x)=1+xg(x)phi(x)" where "lim(x to 0) g(x)=a an...

    Text Solution

    |

  14. What is lim(xto(pi)/(6)) (2sin^(2)x+sinx-1)/(2sin^(2)x-3sinx+1) to?

    Text Solution

    |

  15. A function f defined by f(x)=In(sqrt(x^(2)+1-x)) is

    Text Solution

    |

  16. The domain of the function f defined by f(x)=log(x)10 is

    Text Solution

    |

  17. lim(xtooo) (1-cos^(3)4x)/(x^(2)) is equal to

    Text Solution

    |

  18. If f(x)=3^(1+x)," then "f(x)f(y)f(z) is equal to

    Text Solution

    |

  19. The domain of the function f(x)=sqrt((2-x)(x-3)) is

    Text Solution

    |

  20. The value of k which makes f(x)={{:(sinx,xne0),(k,x=0):}"continuous ...

    Text Solution

    |