Home
Class 12
MATHS
Show that : lim(xto0)[(1)/(x)-(log(1+x...

Show that :
`lim_(xto0)[(1)/(x)-(log(1+x))/(x^(2))]=(1)/(2)`

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2017 (UNIT-1)|4 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2017 (UNIT-2)|6 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • METHOD OF SUBSTITUTION

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

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

Show that : lim_(xto0)(10^(x)-2^(x)-5^(x)+1)/(x^(2))=log_(e)2.log_(e)5

Show that : lim_(xto0)(sinlog(1+x))/(log(1+sinx))=1

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

Evaluate lim_(xto0) (e^(x^(2))-cosx)/(x^(2))

Evaluate lim_(xto0) (e^(x)+e^(-x)-2)/(x^(2))

lim _(xto0) (a ^(x) -b^(x))/(e ^(x)-1)

Evaluate lim_(xto0) ((1)/(x^(2))-(1)/(sin^(2)x)).

Prove that: lim_(xto0)(p^(x)-q^(x))/(tanx)=log"(p)/(q)

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

Prove that: lim_(xto0)log(1+2x)/(sin3x)=(2)/(3)

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-CALCULUS
  1. Show that : lim(xto2)(sin(e^(x-2)-1))/(log(x-1))=1

    Text Solution

    |

  2. Show that : lim(xto""pi)(sqrt(2+cosx)-1)/((pi-x)^(2))=(1)/(4)

    Text Solution

    |

  3. Show that : lim(xto0)[(1)/(x)-(log(1+x))/(x^(2))]=(1)/(2)

    Text Solution

    |

  4. Show that : lim(xto(pi)/(4))(sqrt2-(sinx+cosx))/((4x-pi)^(2))=(1)/(1...

    Text Solution

    |

  5. If f(x)=lim(ntooo)(x^(n)g(x)+h(x))/(x^(n)+1) show that f(x) =h(x), wh...

    Text Solution

    |

  6. If lim(xto0)(sin2x+asinx)/(x^(3)) is finite, find a and the limit.

    Text Solution

    |

  7. Evaluate the following limits: lim(xto0)(sqrt(x^2-1)+sqrt(x-1))/(sqr...

    Text Solution

    |

  8. Evaluate the following limits: lim(xto2a)(sqrt(x-2a)+sqrtx-sqrt2a)/(...

    Text Solution

    |

  9. Evaluate the following limits: lim(xto0)(sinx^(2)(1-cosx^(2)))/(x^(6...

    Text Solution

    |

  10. Evaluate the following limits: lim(xto0)(xe^(x)-log(1+x))/(x^(2))

    Text Solution

    |

  11. Evaluate the following limits: lim(hto0)((a+h)^(2)sin(a+h)-a^(2)sina...

    Text Solution

    |

  12. Evaluate the following limits: lim(ntooo)[(n)/(n^(2))+(n+1)/(n^(2))+...

    Text Solution

    |

  13. Evaluate the following limits: lim(xto3)(3-sqrt(6+x))/(3sqrt3-sqrt(6...

    Text Solution

    |

  14. Evaluate the following limits: lim(xto0)(sqrt(cosx)-root3cosx)/(sin^...

    Text Solution

    |

  15. Evaluate the following limits: lim(xto0)[coec^(3)xcotx-2cot^(3)xcose...

    Text Solution

    |

  16. Evaluate the following limits: lim(xto(pi)/(2))(xtanx-(pi)/(2)secx)

    Text Solution

    |

  17. Show that lim(xto1)(sqrt(1-cos(x-1)))/(x-1) does not exist.

    Text Solution

    |

  18. Evaluate: lim(xto2)(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))

    Text Solution

    |

  19. Evaluate: lim(xto(pi)/(2))((2xsecx)/(pi)-tanx)

    Text Solution

    |

  20. Evaluate: lim(xto0)(cosx)^(cot^(2)x)

    Text Solution

    |