Home
Class 12
MATHS
Evaluate : underset(hrarr0)"lim"(f(1+h)-...

Evaluate : `underset(hrarr0)"lim"(f(1+h)-f(1))/(2h) , " where" f(x) =(1)/(x)` .

Text Solution

Verified by Experts

The correct Answer is:
`-1/2`
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

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

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

Evaluate : underset(hrarr0)"lim"e^(2)h^(2-3h+2)

underset(hrarr1)"lim"(2h^(2)-2h+9)^(3/2)= ?

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

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

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)

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

Evaluate the following limits : underset(hrarr0)"lim"(1-cosh)/(h" sin "h)

CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Evaluate : underset(xrarr2)"lim"(x-sqrt(3x-2))/(x^(2)-4)

    Text Solution

    |

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

    Text Solution

    |

  3. Evaluate : underset(hrarr0)"lim"(f(1+h)-f(1))/(2h) , " where" f(x) =(1...

    Text Solution

    |

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

    Text Solution

    |

  5. Evaluate : underset(xrarr3)"lim"(sqrt(x-3)+sqrt(x)-sqrt(3))/(sqrt(x...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that underset(xrarr0)"lim"((1+x)^(1//2)-1)/((1+x)^(1//3)-1)=(3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |