Home
Class 12
MATHS
If the function f(x) = {((sin 3x)/x, x n...

If the function `f(x) = {((sin 3x)/x, x ne 0),(k/x, x = 0):}` is continuous at x = 0, then k =

A

0

B

e

C

`1/e^(2)`

D

`e^(1/3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos
  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

The function f(x) {((sin x)/x + cos x, x ne 0), (k, x = 0):} is continuous at x = 0, then the value of k is

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

If f(x) = {((x^(5)-32)/(x-2), x ne 2),(k, x =2):} is continuous at x = 2, then k =

If f(x) = {((sin 5x)/(x^(2)+2x), x ne 0),(k+1/2, x =0):} is continuous at x = 0, then the value of k is

If f(x)={((1-cosx)/(x),xne0),(k, x=0):} is continuous at x=0 then k=

The function f(x) = {{:((sin x)/(x) + cos x,"if",x ne 0),(k,"if",x = 0):} is continuous at x = 0, then value of k is :

Let f(x) = {((sin pix)/(5x), x ne 0),(k, x =0):} If f(x) is continuous at x =0, then the value of k is

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

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

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. To make f(x)=(x+1)^(cotx) continuous at x=0,f(0) must defined as

    Text Solution

    |

  2. The function f(x)=|x-2|+x is

    Text Solution

    |

  3. If the function f(x) = {((sin 3x)/x, x ne 0),(k/x, x = 0):} is continu...

    Text Solution

    |

  4. Let f(x) = (1 - cos px)/(x sin x), where x ne 0 and f(0) = (1)/(2). If...

    Text Solution

    |

  5. Let f(x) = [(x^(2),x le 0),(ax + b, x gt 0)]lim The values of a and b ...

    Text Solution

    |

  6. If the function f(x) ={(ax-b, x le1),(3x, 1lt x lt 2),(bx^(2)-a, x ge ...

    Text Solution

    |

  7. y = tan^(-1)((3x-x^3)/(1-3x^2)), 1/(sqrt3) , x , 1/(sqrt3).

    Text Solution

    |

  8. f(x) = {((sin 2x)^(tan^(2)2x), x ne pi/4),(k, x = pi/4):}. If f(x) is ...

    Text Solution

    |

  9. If f(x) = {((x^(5)-32)/(x-2), x ne 2),(k, x =2):} is continuous at x =...

    Text Solution

    |

  10. If the function f(x) = [((cos x)^(1//x),x ne 0),(k,x = 0):} is continu...

    Text Solution

    |

  11. If f(x) ={(3x-4, 0lexle2),(2x+lambda, 2ltxle3):} is continuous at x = ...

    Text Solution

    |

  12. If f(x) = (2x^(3)-ax+3)/(x-3) is continuous at x = 3, then

    Text Solution

    |

  13. If [x]^(2)-5[x]+6=0, where [.] denotes the greatest integer function, ...

    Text Solution

    |

  14. lim(x rarr oo) (log x)/([x]), where [.] denotes the greatest integer f...

    Text Solution

    |

  15. If f(x) is an odd function and lim(x rarr 0) f(x) exists, then lim(x r...

    Text Solution

    |

  16. lim(x rarr 0) (sin x)/(x (1 + cos x)) is equal to :

    Text Solution

    |

  17. lim(x rarr (pi)/(2)) (1-sin x)/(cos x) is equal to :

    Text Solution

    |

  18. lim(x rarr 0) (|x|)/(x) is equal to :

    Text Solution

    |

  19. lim(x rarr 1) [x-1], where [*] is the greatest integer function is equ...

    Text Solution

    |

  20. lim(x rarr 0)"x sin" (1)/(x) is equal to :

    Text Solution

    |