Home
Class 12
MATHS
If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x...

If `f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4))` in `[-1, 1] - {0}`, then for removable discontinuity of f at `x=0, f(0)=`

A

4 log 8

B

8 log 2

C

`4 (log 8)^(2)`

D

`8 (log 2)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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

f(x)=((2^(x)-1)^(2))/(tan x log(1+x)),x!=0 and f(x)=2log2,x=0 at x=0 is:

If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0):} , then

If f(x)=(e^(2x)-(1+4x)^(1/2))/(ln(1-x^(2))) for x!=0, then f has

Show the function, f(x) = {{:((e^(1//x)-1)/(e^(1//x)+1)",","when",x ne 0),(0",","when",x = 0):} has non-removable discontinuity at x = 0

If f(x) {:( =((2^(x)-1)^(2))/(sin x.log(1+x))", if " x != 0 ),(= 2 log 2", if " x = 0 " ) :} then , at x = 0 the function f is

If f(x)=sin^(-1)((2^(x+1))/(1+4^(x))), find f'(0)

The function f(x)=((3^(x)-1)^(2))/(sin x*ln(1+x)),x!=0, is continuous at x=0, Then the value of f(0) is

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

    Text Solution

    |

  2. If f(x) is continous at x=0, where f(x) ((e^(3x)-1)sin x)/(xlog(1+x)),...

    Text Solution

    |

  3. If f(x)=((8^(x)-1)^(2))/(sin x log (1+ x/4)) in [-1, 1] - {0}, then f...

    Text Solution

    |

  4. If f(x) is continuous at x=0, where f(x)=((4^(sin x)-1)^(2))/(x log (...

    Text Solution

    |

  5. If f(x) is continuous at x=0, where f(x)=((3^(sin x)-1)^(2))/(x log (...

    Text Solution

    |

  6. If f(x) is continuous at x=0, where f(x)={:{(((e^(x)-1)^(4))/(sin(x^(2...

    Text Solution

    |

  7. If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for x in [(-pi)/(2), (pi)/(2)]-{0}...

    Text Solution

    |

  8. The function defined by f(x)={:{((1+tan^(2)sqrt(x))^((1)/(2x))", for "...

    Text Solution

    |

  9. The function defined by f(x)={((x^(2)+e^((1)/(2-x)))^(-1)",",x ne 2)...

    Text Solution

    |

  10. If f(x)=x^(2)-sin x+5, then at x=pi

    Text Solution

    |

  11. If f(x)={:{(x", for " 0 le x lt 1/2),(1-x", for " 1/2 le x lt 1):} , t...

    Text Solution

    |

  12. If f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt x lt 3),(x+3", for " 3 le x l...

    Text Solution

    |

  13. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

    Text Solution

    |

  14. If f(x)={:{(x-1", for " 1 le x lt 2),(2x+3", for " 2 le x le 3):}, the...

    Text Solution

    |

  15. If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " p...

    Text Solution

    |

  16. If f(x) is continuous at x=0, where f(x)={((sin x)/(x)+cos x", for " ...

    Text Solution

    |

  17. If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):}, then

    Text Solution

    |

  18. If f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):}, t...

    Text Solution

    |

  19. If f(x)={:{(x-1", for " 1 le x lt 2),(2", for " x=2),(2x-3", for " 2 l...

    Text Solution

    |

  20. If f(x)={:{(x^(2)", for " x le 1),(x+3", for " x gt 1):}, then at x=1

    Text Solution

    |