Home
Class 12
MATHS
If underset(xrarr0)"lim"(1+x)^(1//x)=e ...

If `underset(xrarr0)"lim"(1+x)^(1//x)=e` , show that
`underset(xrarr0)"lim"(1+4x)^(1//x)=e^4`

Promotional Banner

Topper's Solved these Questions

  • LIMIT

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

  • LIMIT

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Integer Answer Type )|5 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 ( Short Answer Type Questions)|80 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

If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0)"lim"(1+2x)^(1//x)=e^(2)

If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0)"lim"(1+3x)^(3//x)=e^(9)

If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr1)"lim"x^((1)/(1-x))=e^(-1)

underset(xrarr0)"lim"(log(1+4x))/(x) =

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

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

underset(xrarr0)"lim"(sin3x)/(sinx) =

underset(xrarr 0)"lim"(sin^(-1)x)/(x) =

Show that underset(xrarr1)"lim"(1)/(x-1)^(2)=+oo .

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

CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Do the following limits exist ? underset(xrarr0)"lim""Xcos"(1)/(x)

    Text Solution

    |

  2. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

    Text Solution

    |

  3. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

    Text Solution

    |

  4. Prove : underset(xrarr0)"lim""xcos"(1)/(x)=0

    Text Solution

    |

  5. Prove : underset(xrarr0)"lim"x^(2)"sin"(1)/(x)=0

    Text Solution

    |

  6. Prove : underset(xrarr0)"lim"(x^(2)sin^(1/x))=0

    Text Solution

    |

  7. Prove : underset(xrarroo)"lim"(sinx)/(x)=0

    Text Solution

    |

  8. Prove : underset(xrarroo)"lim"(cosx)/(x)=0

    Text Solution

    |

  9. Putting z=x-(pi)/(4)" show that "underset(xrarr(pi)/(4))"lim"(1-tanx)/...

    Text Solution

    |

  10. Putting x=theta-(pi)/(4)" prove that "underset(thetararr(pi)/(4))"lim"...

    Text Solution

    |

  11. A function f (x) is defined as follwos : f(x){:(=1,","" when " xne0...

    Text Solution

    |

  12. Prove : underset(xrarr1)"lim"(4^(x)-4)/(x-1)=8log(e)2

    Text Solution

    |

  13. Prove : underset(xrarr2)"lim"(log(2x-3))/(2(x-2))=1

    Text Solution

    |

  14. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

    Text Solution

    |

  15. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

    Text Solution

    |

  16. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr1...

    Text Solution

    |

  17. If underset(xrarr0)"lim"(1+x)^(1//x)=e , show that underset(xrarr0...

    Text Solution

    |

  18. If f(x)=underset(nrarroo)"lim"(1)/(1+nsin^(2)pix) , find f (x) for all...

    Text Solution

    |

  19. Prove : underset(xrarroo)"lim"(sinx)/(x)=0

    Text Solution

    |

  20. Evaluate the following limits : underset(x to 0) lim (e^(px)-e^(-qx)...

    Text Solution

    |