Home
Class 12
MATHS
Prove that underset(hrarr0)"lim"(root3...

Prove that
`underset(hrarr0)"lim"(root3(x+h)-root3(x))/(h)=(1)/(3)x^(-2/3)`

Promotional Banner

Topper's Solved these Questions

  • LIMIT

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

  • LIMIT

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

  • LIMIT

    CHHAYA PUBLICATION|Exercise EXAMPLE|38 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

show : underset(xrarra)"lim"(root(3)(x)-root(3)(a))/(x-a)=(1)/(3)a^(-2/3)

show : underset(hrarr0)"lim"(root(3)(h+1)-1)/(h)=(1)/(3)

If f(x)=(1)/(x) , prove that , underset(hrarr0)"lim"(f(2+h)-f(2))/(h)=-(1)/(4)

Evaluate : underset(xrarr0)"lim"(root(3)(1+x)-root(3)(1-x))/(x)

Prove : underset(nrarroo)"lim"[root(3)(n+1)-root(3)(n)]=0

Prove that : underset(xrarr3)"lim"(x^(2)-9)/(x-3)=6

underset(hrarr3)"lim"root(3)(2h^(2)-3h-1)= ?

underset(hrarr0)"lim"(3h^(2)-2h)/(h)= ?

Prove that underset(hrarr-2)"lim"(h^(5)+32)/(h+2)=80

Prove : underset(hrarr0)"lim"(sec(x+h)-secx)/(h)=sec x tanx

CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Prove that underset(xrarr0)"lim"((1+x)^(1//2)-1)/((1+x)^(1//3)-1)=(3...

    Text Solution

    |

  2. Prove that underset(xrarry)"lim"(x^(9//2)-y^(9//2))/(x^(5//2)-y^(5//...

    Text Solution

    |

  3. Prove that underset(hrarr0)"lim"(root3(x+h)-root3(x))/(h)=(1)/(3)x^(...

    Text Solution

    |

  4. Prove that underset(xrarra)"lim"((x+5)^(5//2)-(a+5)^(5//2))/(x-a)=(...

    Text Solution

    |

  5. Evaluate : underset(xrarr0)"lim"(root(3)(1+x)-root(3)(1-x))/(x)

    Text Solution

    |

  6. Evaluate : underset(xrarr2)"lim"(2-sqrt(2+x))/(root(3)(2)-root(3)(4-x)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. underset(xrarr(pi)/(2))"lim"(cosx)/((pi)/(2)-x) =

    Text Solution

    |

  10. Evaluate :underset(xrarrpi)"lim"(sin3x)/(sin2x)

    Text Solution

    |

  11. Evaluate :underset(xrarrpi)"lim"(1+cosx)/(x-pi)^(2)

    Text Solution

    |

  12. Evaluate :underset(xrarr0)"lim"(sinx(1-cosx))/(x^(3))

    Text Solution

    |

  13. Evaluate :underset(xrarr0)"lim"(x^(2)-tan2x)/(tanx)

    Text Solution

    |

  14. Evaluate :underset(xrarr0)"lim"(cosec"x-cotx)/(x)

    Text Solution

    |

  15. Evaluate :underset(xrarr0)"lim"(cos5x-cos7x)/(cosx-cos5x)

    Text Solution

    |

  16. Evaluate :underset(xrarry)"lim"(sin^(2)x-sin^(2)y)/(x^(2)-y^(2))

    Text Solution

    |

  17. Evaluate : underset(xrarr(pi)/(2))"lim"((pi)/(2)-x)tanx

    Text Solution

    |

  18. Evaluate : underset(xrarr1)"lim"(1-x)"tan"(pix)/(2)

    Text Solution

    |

  19. Evaluate : underset(xrarra)"lim"(xsina-asinx)/(x-a)

    Text Solution

    |

  20. Evaluate : underset(hrarr0)"lim"(e^(5h)-1)/(3h)

    Text Solution

    |