Home
Class 12
MATHS
The limit of [(1)/(x^(2))+((2)^(x))/(e^(...

The limit of `[(1)/(x^(2))+((2)^(x))/(e^(x)-1)-(1)/(e^(x)-1)]` as `x rarr0`

A

approaches `+oo`

B

approaches `-oo`

C

is equal to `log_(e)2`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 2 : SINGLE OPTION CORRECT TYPE)|5 Videos
  • LIMITS AND CONTINUITY

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|2 Videos
  • LIMITS AND CONTINUITY

    MTG-WBJEE|Exercise WB JEE WORKOUT (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|10 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    MTG-WBJEE|Exercise WB JEE Previous Years Questions ( CATEGORY 1 : Single Option Correct Type (1 Mark))|6 Videos
  • LOGARITHMS

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS|10 Videos

Similar Questions

Explore conceptually related problems

The limit of [(1)/(x^(2))+((2013)^(x))/(e^(x)-1)-(1)/(e^(x)-1)] as x rarr0

lim_(x rarr0)((e^(x)-x-1)/(x))

lim_(x rarr0)(e^(x)-x-1)/(x^(2))

The limit of [(1)/(x)sqrt(1+x)-sqrt(1+(1)/(x^(2))]] as x rarr0

The limit of x sin(e^((1)/(x)))asx rarr0

lim_(x rarr0)((ln(1+x^(2)+x^(4)))/((e^(x)-1)x)

lim_(x rarr0)(2^(2x)-1)/(x)

The value of lim_(x rarr0)((1+x)^((1)/(x))-e+(1)/(2)ex)/(x^(2)) is

lim_(x rarr0)(e^((1)/(x))-1)/(e^((1)/(x))+1)

lim_(x rarr0)((1+x+x^(2))-e^(x))/(x^(2))

MTG-WBJEE-LIMITS AND CONTINUITY-WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 1 : SINGLE OPTION CORRECT TYPE)
  1. The limit of [(1)/(x^(2))+((2)^(x))/(e^(x)-1)-(1)/(e^(x)-1)] as x rarr...

    Text Solution

    |

  2. The limit of [(1)/(x)sqrt(1+x)-sqrt(1+(1)/(x^(2))]] as x rarr0

    Text Solution

    |

  3. The limit of x sin (e^(-1//x)) as x rarr0

    Text Solution

    |

  4. The limit of sum(n=1)^(1000)(-1)^(n)x^(n) as x rarroo

    Text Solution

    |

  5. The function f(x)=(tan{pi[x-(pi)/(2)]})/(2+[x]^(2)), where [x] denotes...

    Text Solution

    |

  6. LEt f(x) be a differentiable function and f'(4)=5. Then, lim(x->2)(f(4...

    Text Solution

    |

  7. If lim(xrarr0)(2a sin x-sin 2x)/(tan^(3)x) exists and is equal to 1, t...

    Text Solution

    |

  8. Let [x] denote the greatest integer less than or equal to x for any re...

    Text Solution

    |

  9. If lim(xrarr0)(axe^(x)-b log(1+x))/(x^(2))=3, then the value of a and ...

    Text Solution

    |

  10. Let f : R -> R be defined as f(x)={0, x is irrational sin|x|, x is ...

    Text Solution

    |

  11. Let x(n)=(1-(1)/(3))^(2)(1-(1)/(6))^(2)(1-(1)/(10))^(2)…(1-(1)/((n(n+1...

    Text Solution

    |

  12. Let [x] denote the greatest integer less than or equal to x. Then the ...

    Text Solution

    |

  13. Let f:[-2, 2]rarrR be a continuous function such that f(x) assumes onl...

    Text Solution

    |

  14. lim(x rarr 1)((1+x)/(2+x))^((1-sqrt(x))/(1-x))

    Text Solution

    |

  15. the value of lim(n->oo) {sqrt(n+1)+sqrt(n+2)+...........+sqrt(2n-1)}/n...

    Text Solution

    |

  16. If f''(x)=k,k != 0 , then the value of lim(x->0)(2f(x)-3f(2x)+f(4x))...

    Text Solution

    |

  17. lim(xrarr0)(sinx)^(2tanx)

    Text Solution

    |

  18. The value of lim(n->oo)[n/(n^2+1^2)+n/(n^2+2^2)++1/(2n)] is

    Text Solution

    |

  19. f(x) = 3x^10 – 7x^8+ 5x^6 -21x^3 + 3x^2 –7, then is the value of lim(...

    Text Solution

    |

  20. Let f:[a, b] rarrR be such that f is differentiable in (a, b), f is co...

    Text Solution

    |