Home
Class 12
MATHS
If lim(x to 0)(1+x)^(1/x)=e, prove that ...

If `lim_(x to 0)(1+x)^(1/x)=e,` prove that `lim_(x to 0)(1+3x)^(((x+2))/(x))=e^(6).`

Promotional Banner

Topper's Solved these Questions

  • LIMIT

    CHHAYA PUBLICATION|Exercise IIIustrative Examples|53 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXERCISE 2 (Multiple Choice Type Questions)|20 Videos

  • LIMIT

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion- Reason Type)|3 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

lim_(x to 0)(1+4x)^((x+2)/(x))=e^(8)

Prove that lim_(xto0)(1+3x)^(3/x)=e^(9)

lim_(x to 0) (e^(13x)-e^(7x))/x

lim_(xto0+)(e^x+x)^((1)/(x))

prove that lim_(x rarr 0) (1+2x)^(1/x)=e^(2)

Prove that: lim_(x to0)log(1+sinx)/(x)=1

If lim_(x to 0)x^((1)/(1-x))=e^(-1)

Prove that lim_(xrarroo)(1+1/x)^x=e

The value of lim_(x to 0)(1+3x)^((x+2)/(x)) is -

Using lim_(x to 0)(e^(x)-1)/(x)=1 , show that, lim_(x to 0)log_(e)(1+x)/(x)=1

CHHAYA PUBLICATION-LIMIT-EXAMPLE
  1. Show that , lim(x rarr 0)(3^(x)+3^(-x)-2)/(x^(2)

    Text Solution

    |

  2. Show that, lim(x rarr 0) log(1+x^(3))/(sin^(3)x)= 1

    Text Solution

    |

  3. If lim(x to 0)(1+x)^(1/x)=e, prove that lim(x to 0)(1+3x)^(((x+2))/(x)...

    Text Solution

    |

  4. Evaluate the following limits: lim(x to 3)sin(e^(x-3)-1)/(log(x-2))

    Text Solution

    |

  5. Evaluate the following limits: lim(x to 0)[(1)/(x)-log(1+x)/(x^(2))]

    Text Solution

    |

  6. Evaluate the following limits: lim(x rarr 0)(xe^(x)-log(1+x))/(x^(2))

    Text Solution

    |

  7. Find the value of : lim(x rarr oo) ((x+5)/(x+1))^(5)

    Text Solution

    |

  8. Find the value of : lim(x rarr oo) ((x+5)/(x-1))^(5)

    Text Solution

    |

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

    Text Solution

    |

  10. Does underset(xrarr2)"lim"(x^(2)-4)/(x-2) exist If so , find its val...

    Text Solution

    |

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

    Text Solution

    |

  12. Draw the graph of y=f(x)=(x^(2))/(x) and from the graph examine wheth...

    Text Solution

    |

  13. Draw the graph of the function f(x)=(|x|)/(x) and from the graph disc...

    Text Solution

    |

  14. Let f(x){:(=x^(2),","" when "xlt1),(=1,",""when "xle1):} Draw t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Evaluate : underset(xrarr-oo)"lim"(1+(2)/(x^(2))).

    Text Solution

    |

  18. Prove that underset(xrarroo)"lim"(1)/(x)=0.

    Text Solution

    |

  19. Show that underset(xrarr2)"lim"(x^(2)-3x+5)=3.

    Text Solution

    |

  20. Prove that underset(xrarr2)"lim"(x^(2)-3x+5)=3. Where n is a positive ...

    Text Solution

    |