Home
Class 12
MATHS
If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3))...

If `{:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):}`
is continuous at x = 0, then k =

A

2

B

`-2`

C

`+- 2`

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Critical Thinking|80 Videos

  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

Similar Questions

Explore conceptually related problems

If {:(f(x),=(e^(5x)-e^(2x))/(sin 3x),",",x != 0),(,=k/2, ",",x = 0):} is continuous at x = 0, the value of k is

{:(f(x),=(log(1+kx))/(sin x),",",x != 0),(,=5, ",",x = 0):} If f is continuous at x = 0, then k =

If {:(f(x),=((4x+1)/(1-4x))^(1/x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then k =

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

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

If f(x) = {:((8^(x)-2^(x))/(k^(x)-1)", if " x != 0 ),(=2", if " x = 0 ):} is continuous at x = 0, then k = ….

If the function {:(f(x),=[log((pi)/4+x)]^(1/x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0, then k = ?

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),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then the value of k is

TARGET PUBLICATION-CONTINUITY-Competitive Thinking
  1. If f(x) = {((log(e )x)/(x-1), ",", x != 1),(k, ",", x = 1):} is contin...

    Text Solution

    |

  2. The function f(x) = (1-sin x + cos x)/(1+sin x + cosx) is not defined ...

    Text Solution

    |

  3. If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):...

    Text Solution

    |

  4. If f(x) = (e^(x^2)-cos x)/(x^(2)), "for" x != 0 is continuous at x = 0...

    Text Solution

    |

  5. For what value of k, the function defined by {:(f(x),=(log(1+2x)sinx^(...

    Text Solution

    |

  6. If {:(f(x),=log(1-3x)(1+3x),",",x != 0),(,=k, ",",x = 0):} is contin...

    Text Solution

    |

  7. If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x =...

    Text Solution

    |

  8. If the function {:(f(x),=[log((pi)/4+x)]^(1/x),",","for"x != 0),(,=k, ...

    Text Solution

    |

  9. Function f(x) = {((log(2)2x)^(log(x)8), ",", x != 1),((k-1)^(3), ",", ...

    Text Solution

    |

  10. For the function f(x) = (log(e )(1+x)-log(e )(1-x))/(x) to be continuo...

    Text Solution

    |

  11. The function f(x) = (log(1+ax)-log(1-bx))/(x) is not defined at x = 0....

    Text Solution

    |

  12. If the function f(x) = {((x^(2)-(A+2)x+A)/(x-2), ",", x != 2),(2, ",",...

    Text Solution

    |

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

    Text Solution

    |

  14. If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0)...

    Text Solution

    |

  15. If f(x) = {(ax^(2)-b, ",", "when" 0 le x le 1),(2, ",","when"x = 1),(x...

    Text Solution

    |

  16. If f(x) = {(sin x, ",", "if" x le 0),(x^(2)+a^(2), ",", "if" 0 lt x l...

    Text Solution

    |

  17. If f(x) = {((1-sinzx)/(pi-2x), ",", x != pi/2),(lambda, ",", x = pi/2...

    Text Solution

    |

  18. If a function of defined by f(x) = {((1-sinzx)/(pi-2x), ",","if" x != ...

    Text Solution

    |

  19. Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",", x = p...

    Text Solution

    |

  20. if f(x)=sin[x]/([x]+1) , x > 0 and f(x)=(cospi/2[x])/([x]) , x < 0 and...

    Text Solution

    |