Home
Class 12
MATHS
Evaluate : underset(xrarr0)"lim"(2^(x)-1...

Evaluate : `underset(xrarr0)"lim"(2^(x)-1)/(sqrt(1+x)-1)`

Text Solution

Verified by Experts

The correct Answer is:
`2log2`
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 ( Long Answer Type Questions)|38 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Multiple Correct Answers Type )|5 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 (Very Short Answer Type Questions )|56 Videos

  • LAWS OF INDICES

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|6 Videos

  • LINEAR DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination(E. Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

Evaluate : underset(xrarr0)"lim"(1)/(x) .

Evaluate : underset(xrarr0)"lim"(tanx^(@))/(x)

underset(xrarr0)"lim"(a^(2x)-1)/(x) =

underset(xrarr0)"lim"(e^(3x)-1)/(x) =

Evaluate : underset(xrarr0)"lim"(sin^(-1)x)/(2x)

underset(xrarr1)"lim"(x-1)/(sqrt(x)-1)= ?

Evaluate : underset(xrarr0)"lim"(e^(x^(2))-1)/(sin^(2)x)

Evaluate : underset(xrarr0)"lim"(e^(x)-e^(-x))/(x)

Evaluate : underset(xrarr0)"lim"(sqrt(1-x^(3))-sqrt(1-x))/(sqrt(1+x^(2))-sqrt(1+x))

Evaluate : underset(xrarr0)"lim"(sqrt(1+x^(2))-sqrt(1+x))/(sqrt(1+x^(3))-sqrt(1+x))

CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Short Answer Type Questions)
  1. Evaluate : underset(xrarr0)"lim"(a^(alphax)-b^(betax))/(x)

    Text Solution

    |

  2. Evaluate : underset(xrarr0)"lim"(log(1+3x))/(x)

    Text Solution

    |

  3. Evaluate : underset(xrarr0)"lim"(2^(x)-1)/(sqrt(1+x)-1)

    Text Solution

    |

  4. Evaluate : underset(xrarr0)"lim"(e^(x)+e^(-x)-2)/(x^(2))

    Text Solution

    |

  5. Prove :underset(xrarr0)"lim"(log(1+2x))/(sin3x)=(2)/(3)

    Text Solution

    |

  6. Prove :underset(xrarr1)"lim"(logx)/(x-1)=1

    Text Solution

    |

  7. Prove : underset(xrarre)"lim"(logx-1)/(x-e)=(1)/(e)

    Text Solution

    |

  8. Prove : underset(xrarr0)"lim"(p^(x)-q^(x))/(tanx)="log"(q)/(q)

    Text Solution

    |

  9. Prove :underset(xrarr0)"lim"(sinlog(1+x))/(x)=1

    Text Solution

    |

  10. Prove :underset(xrarr0)"lim"(sinlog(1+x))/(e^(x)-1)=1

    Text Solution

    |

  11. Prove :underset(xrarr0)"lim"(logcosx)/(sin^(2)x)=-(1)/(2)

    Text Solution

    |

  12. Prove :underset(hrarr0)"lim"(log(x+h)-logx)/(h)=(1)/(x)

    Text Solution

    |

  13. Prove :underset(xrarr0)"lim"(log(1+sinx))/(x)=1

    Text Solution

    |

  14. Prove :underset(xrarr0)"lim"(sqrt(1+x)-1)/(log(1+x))=(1)/(2)

    Text Solution

    |

  15. Evaluate : underset(xrarr0)"lim"(sinx)/(log(e)(1+x)^(1/2))

    Text Solution

    |

  16. Evaluate : underset(xrarr0)"lim"(e^(x^(2))-1)/(sin^(2)x)

    Text Solution

    |

  17. Evaluate : underset(xrarr0)"lim"((e^(x)-1)log(1+x))/(sinx)

    Text Solution

    |

  18. Evaluate : underset(xrarr4)"lim"(x^(7//2)-4^(7//2))/(log(e)(x-3))

    Text Solution

    |

  19. Evaluate : underset(xrarr0)"lim"(log(1+alphax))/(sinbetax)

    Text Solution

    |

  20. Evaluate : underset(xrarr0)"lim"(e^(3x)-1)/(log(1+5x))

    Text Solution

    |