Home
Class 12
MATHS
The value of lim(x to 0) ((4^(x) - 1)^(...

The value of `lim_(x to 0) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x^(2))/(3)))` equals

A

`3(log 4)^(3)`

B

`4(log 4)^(3)`

C

`12 (log 4)^(3)`

D

`15 (log 4)^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section - C ( More than one options are correct )|5 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section - D|6 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Assignment ( section -A)|61 Videos
  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos
  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(xrarr0)((4^x-1)^3)/(sin.(x^2)/(4)log(1+3x)) ,is

Evaluate lim_(x to 0) ((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))

The value of lim_(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

lim_(x to 0) (log (1 + 2x))/(x) + lim_(x to 0) (x^(4) - 2^(4))/(x - 2) equals

The value of lim_(xrarr0)(1-cos^(3)x)/(sin^(2)xcos x) is equal to

lim_(x to 1//2) (8x^(3) - 1)/(16 x^(4) - 1) is equal to

The value of lim_(x to 0) (log(sin 5x + cos 5x))/(tan 3x) is equal to

The value of a for which the function f(x)={(((4^x-1)^3)/(sin(x/a)log(1+x^2/3)) ,, x!=0),(12(log4)^3 ,, x=0):} may be continuous at x=0 is :

The value of lim_(xrarr 0) (e^x+log (1+x)-(1-x)^-2)/(x^2) is equal to

The value of lim_(xrarr0^(+))((1-cos(sin^(2)x))/(x^(2)))^((log_(e)(1-2x^(2)))/(sin^(2)x)) is

AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Section -B
  1. lim(x->0)((4^x+9^x)/2)^(1/x)

    Text Solution

    |

  2. If underset (xrarr0)"lim"(cosx+asinbx)^(1/x)=e^(2) then the possible v...

    Text Solution

    |

  3. underset(x to 0)(Lt) (sqrt(1 - cos 2 x))/(sqrt(2)x) =

    Text Solution

    |

  4. lim(x to 2^+) (([x]^(3))/(3) - [(x)/(3)]^(3)) is where [x] represents ...

    Text Solution

    |

  5. The value of lim(x to 0) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x^...

    Text Solution

    |

  6. If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is co...

    Text Solution

    |

  7. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

    Text Solution

    |

  8. The number of points at which the function f(x) = 1/ (log |2x|) is di...

    Text Solution

    |

  9. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

    Text Solution

    |

  10. The set of points where f(x)=x/(1+|x|) is differentiable is

    Text Solution

    |

  11. The function |x^2 - 3x+2| + cos |x| is not differentiableat x=

    Text Solution

    |

  12. At x = 0 , the function y = e^(-|x|) is

    Text Solution

    |

  13. Let f(x) = lambda + mu|x|+nu|x|^2, where lambda,mu, nu in R, then f'(0...

    Text Solution

    |

  14. If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...

    Text Solution

    |

  15. Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the gre...

    Text Solution

    |

  16. A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equ...

    Text Solution

    |

  17. If 3sin(x y)+4cos(x y)=5 , then (dy)/(dx)= (a) y/x (b) (3sin(x y)+4...

    Text Solution

    |

  18. Let f(x) = maximum {4, 1 + x^(2), x^(2) -1}, AA x in R. Then, the tota...

    Text Solution

    |

  19. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)).Find g'(x) in te...

    Text Solution

    |

  20. If f is a real- valued differentiable function satisfying |f(x) - f(y)...

    Text Solution

    |