Home
Class 12
MATHS
If f(x) is continuous at x=16, where f(...

If `f(x)` is continuous at `x=16`, where `f(x)={:{((x^(8)-(256)^(4))/(x^(4)-(16)^(4))", for" x!=16),(k ", for" x=16) :}` , then `k=`

A

`(16)^(4)`

B

`2(16)^(4)`

C

`4(16)^(4)`

D

`3(16)^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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 f(x) is continuous at x=0 , where f(x)={:{(((e^(x)-1)^(4))/(sin(x^(2)/k^(2))log(1+ x^(2)/(2)))", for " x!=0),(8", for " x=0):} , then k=

If f(x) is continuous at x=2 , where f(x)=((x^(2)-x-2)^(20))/((x^(3)-12x+16)^(10)) , for x!=2 , then f(2)=

(x^(4)-16)-:(x+2)

If f(x) is continuous at x=0 , where f(x)={:{((1-cos 4x)/(x^(2))", for " x lt 0),(k", for " x =0),((sqrt(x))/(sqrt(16+sqrt(x))-4)", for " x gt 0):} , then k=

If f(x) is continuous at x=1 , where f(x)={:{(k+x", for " x lt 1),(4x+3", for " x ge 1):} , then k=

prove that f(x) is a continuous funcation where f(x) {{:( (x^(4)-16)/(x-2)",", if , xne 2),( 32 ",", if , x =2):}

int x^4/(x^4-16) dx

The value of ((256x^(16))/(81y^(4)))^(-(1)/(4))' is

lim_(x rarr2)(x^(3)-3x^(2)+4)/(x^(4)-8x^(2)+16)

f(x) ={{:((2^(x+2)-16)/(4^(x)-16), if x ne 2 ),(k, if x = 2):} , x = 2 .

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. Examine the continuity of the given function at given points f(x)=(x+3...

    Text Solution

    |

  2. If f(x) is continuous at x=3, where f(x)={:{((x^(2)-9)/(x-3),", for"x...

    Text Solution

    |

  3. If f(x) is continuous at x=16, where f(x)={:{((x^(8)-(256)^(4))/(x^(4...

    Text Solution

    |

  4. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

    Text Solution

    |

  5. If f(x)=(1+x)^(5//x) is continuous at x=0, then what is the value of f...

    Text Solution

    |

  6. If the function f(x) defined as : f(x) =(x^4-64x)/(sqrt(x^2+9)-5), for...

    Text Solution

    |

  7. The value of f(0), so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

    Text Solution

    |

  8. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(x^2-4a^2)

    Text Solution

    |

  9. If f(x) is continuous at x=sqrt(2), where f(x)=(sqrt(3+2x)-(sqrt(2)+1)...

    Text Solution

    |

  10. If f(x) is continuous at x=5, where f(x)=(sqrt(3+sqrt(4+x))-sqrt(6))/(...

    Text Solution

    |

  11. If f(x) is continuous at x=0, where f(x)=sin x-cos x, for x!=0, then ...

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x) is continuous at x=pi/4, where f(x)=(1-tanx)/(1-sqrt(2)sin x),...

    Text Solution

    |

  14. If f(x) is continuous at x=0 ,where f(x)=(sin(pi cos^(2)x))/(x^(2)) ,f...

    Text Solution

    |

  15. If f(x) is continuous at x=(pi)/(4) where f(x)=(2sqrt(2)-(cos x+sin x)...

    Text Solution

    |

  16. If f(x) is continuous at theta= pi/4, where f(theta)={:{((1-tan theta...

    Text Solution

    |

  17. The function f(x)=(1-sinx+cosx)/(1+sinx+cosx) is not defined at x=pi....

    Text Solution

    |

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

    Text Solution

    |

  19. If f(x) is continuous at x= pi/4, where f(x)=(cos x- sin x)/(cos 2x),...

    Text Solution

    |

  20. If f(x) is continuous at x= pi/4, where f(x)=(2-cosec^(2)x)/(cot x-1)...

    Text Solution

    |